Republicans on Tuesday debuted their full 2014 budget, an ambitious proposal that would seek to balance the budget within a decade, but which is also almost certain to never become law.

Rep. Paul Ryan, R-Wis., the Republican budget chief and 2012 vice presidential nominee, called his third budget an "invitation" to President Barack Obama and Senate Democrats to begin bargaining toward a deal to balance the budget. 

"This is not only a responsible, reasonable, balanced plan," Ryan said, "it's also an invitation. This is an invitation to the president of the United States, to the Senate Democrats to come together to fix these problems."

But just as Obama has made new overtures to Ryan and other Capitol Hill Republicans in hopes of breaking the fiscal logjam in Congress, Ryan produced a new budget that offers up few concessions to Democrats, and doubles down upon many of the policies on which Republicans campaigned during last fall's election.

The new Ryan budget calls for repealing Obama's signature health care reform law, and sweeping changes to Medicare for anyone under the age of 54 -- familiar policies for which Republicans have aggressively pushed during the last two years. The budget's goal would be to eliminate all but two income tax brackets, one at 10 percent and the other at 25 percent; it would raise no new revenue through taxes, cutting against the president's own demands for additional revenue.

Click here for the full text of the budget (.pdf)

"While the House Republican budget aims to reduce the deficit, the math just doesn't add up," White House press secretary Jay Carney said in a statement.

But the White House stopped short of waging a blistering assault on the Ryan plan, offering a glimmer of hope that bipartisanship might still eventually carry the day. 

"While the president disagrees with the House Republican approach, we all agree we need to leave a better future for our children," Carney said. "The president will continue to work with Republicans and Democrats in Congress to grow the economy and cut the deficit in a balanced way."

Still, Ryan defended the generally unflinching conservatism of his budget.

"That means we surrender our principles? That means we stop believing in what we believe in?" he asked at a press conference to debut his proposals. "Elections do have consequences ... This is our offer, this is our vision."

The GOP proposal comes amid new overtures by Obama to Republicans in Congress. The president had lunch last week with Ryan, and dinner with a group of GOP senators. Obama will address House and Senate Republicans separately this week, marking a pivot in his strategy toward vexing fiscal issues following bruising battles over the fiscal cliff during the first two months of this year.

Related: Ryan plan sparks budget battle

This latest GOP plan -- the third authored by Ryan since Republicans retook the House in 2010 -- is the opening salvo in a spring full of budget battles, culminating in the mid-May expiration of the nation's borrowing authority. Congress authorized a suspension of the debt limit through that deadline, but made it contingent upon the House and Senate each passing their own budget. (Republicans have repeatedly needled Senate Democrats for failing to pass a budget in recent years.)

"I hate to break the suspense, but their budget won't balance—ever," Ryan wrote in an op-ed for the Wall Street Journal. "We House Republicans have done our part … Now we invite the president and Senate Democrats to join in the effort."

Mandel Ngan / Mandel Ngan / AFP - Getty Images

House Budget Committee Chairman Paul Ryan makes his way to the West Wing on March 7, 2013 for a lunch with President Barack Obama.

Ryan's blueprint claims to achieve $4.6 trillion in savings over through 2023, and steadily reduce government spending as a share of gross domestic product in the meantime. In his op-ed, Ryan asserted the reforms could boost gross national product by as much as 1.7 percent.  Ryan's previous plan projected a balanced budget outside of ten years. 

But the plan also relies on savings accrued from two plans which Republicans had staunchly opposed: the new taxes on the wealthy in the Jan. 1 fiscal cliff deal, and the $715 billion in savings from cuts to Medicare providers as part of Obama's health care reform law. 

Of the new taxes, Ryan said that Republicans were "not going to re-fight the past." When pressed as to how that principle squares with his budget's goal of repealing Obamacare, Ryan pivoted, and said that the health reform law would be so onerous, that the eventual GOP replacement would be an improvement. 

It would achieve its goal through a series of sweeping reforms, most of which are unlikely to survive the Democratic Senate or a presidential veto threat.

Ryan's budget again seeks changes to Medicare, namely by establishing an exchange of private plans (including traditional Medicare) from which seniors could choose, with the assistance of a premium support voucher. The plan would apply for those under the age of 54 — a threshold one year younger than past Ryan proposals — and also employ means-testing, in which wealthier seniors pay a higher share of their premiums.

The Ryan budget also calls for repealing the health care reform law (though it would leave in place savings from cuts in payments to medical providers, a component against which Ryan and Mitt Romney railed during last fall's campaign).

Related: From continuing resolutions to budget blueprints: What you need to know about money wrangling

The campaign also focused heavily on Ryan's past budgets, as Obama and Democratic candidates downballot railed against similar proposed changes to entitlement programs. Those attacks offered a vivid illustration of the political difficulties in putting such aggressive reform plans to paper. That experience helped inform the GOP's demand that Democrats produce their own alternative budget, through which Republican staffers will surely comb to exploit politically.

Ryan's own budget isn't short on additional conservative prescriptions, either. The 2014 budget calls for sweeping tax reform, with a goal of cutting the top corporate tax rate to 25 percent, and simplifying the income tax into two brackets. The tax cuts would be financed by closing loopholes and deductions in the tax code.

The Republican budget will also touch upon other social programs. It would block-grant Medicaid to states, and allow states more flexibility, too, in implementing welfare programs. Ryan's plan would also freeze the current maximum support for students awarded as Pell Grants, a popular program with students (and young voters) that Obama had expanded in his first term.

The proposals, as a whole, amount to a deeply conservative set of proposals offered against the backdrop of new hopes for bipartisan fiscal talks in Washington.

Obama's renewed outreach — and Republicans' relatively warm reception of it — has stoked the embers of hope that lawmakers may finally reach the kind of grand fiscal deal that has eluded them during the past few years. As Ryan unveils his new budget, Obama's own reaction could either preserve these renewed hopes, or allow them to wither after just a few days.

To that end, Obama was set to speak to House Republicans on Wednesday, and Senate Republicans on Thursday. He was also scheduled to give an interview to ABC News on Tuesday, which could be his first on-camera reactions to Ryan's new proposal.

This story was originally published on Tue Mar 12, 2013 10:07 AM EDT

Updated at 12:32 a.m. ET: An agreement to stave off the harshest and most immediate consequences of the fiscal cliff won approval in the House late Tuesday. President Barack Obama signed the law on Wednesday night, the battle over which foreshadowed more fights with Congress over spending.

Following a day of hectic wrangling on Capitol Hill — where the prospects for passing the bipartisan, Senate legislation regarding the fiscal cliff hung in the balance for much of New Year's Day — the House voted 257 to 167 to pass the belated compromise measure over the objections of many conservative Republicans.

The legislation takes steps toward resolving the combination of automatic tax hikes and spending cuts that took effect at midnight on Jan. 1. It preserves tax rates as they were at the end of 2012, except for those individuals earning more than $400,000 and households earning over $450,000. It also allows taxes on capital gains and dividends to go up, and extends benefits of the unemployed. Additionally, the Senate bill delays the onset of the "sequester" — the swift, automatic spending cuts — for two months. 

Fiscal cliff compromise leaves few satisfied

"Thanks to the votes of Democrats and Republicans in Congress I will sign a law that raises the taxes on the wealthiest of Americans," Obama said in remarks at the White House Tuesday, "while preventing a middle-class tax hike."

The House vote laid bare some of the internal ideological divisions to plague the GOP over the past two years. More Republican congressmen (151) voted against the Senate bill than for it (85), meaning that Democrats' support was needed to advance the final deal. House Speaker John Boehner, R-Ohio, took the rare step of casting a vote, and did so in favor of the legislation. Rep. Paul Ryan, R-Wis., the former Republican vice presidential nominee, also supported the package. But Boehner's top two lieutenants, Majority Leader Eric Cantor, R-Va., and Majority Whip Kevin McCarthy, R-Calif., each opposed the deal.

"Now the focus turns to spending," Boehner said in a statement following the House vote. "The American people re-elected a Republican majority in the House, and we will use it in 2013 to hold the president accountable for the ‘balanced’ approach he promised, meaning significant spending cuts and reforms to the entitlement programs that are driving our country deeper and deeper into debt."

While the last-minute action on Capitol Hill essentially mitigates much of the risk posed to the U.S. economic recovery by the fiscal cliff, it hardly brings resolution to the bitter and often intractable fight in Washington over taxes and spending. The first half of 2013 will feature battles in Congress over raising the debt limit, continuing basic government funding and the expiration of this two-month delay in the sequester. 

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Obama nodded to those looming fights in his remarks Tuesday evening, renewing his call for "balance" in any solution in the coming year to address deficits and debts. But the president also sternly warned Congress against using the debt ceiling as a bargaining chip, as Republicans had in summer of 2011.

"While I'll negotiate over many things, I will not have another debate with this Congress over whether to pay the bills they have racked up," Obama said.

PhotoBlog: Deal done, Obama heads back to Hawaii with a weary wink

The fiscal cliff itself was the product of discord in Congress resolving those very issues. And the difficulty in attaining even this less ambitious piece of legislation — versus the kind of "grand bargain" Obama had first sought in talks with Republicans — offered a cautionary tale for the 113th Congress, in which the House and the Senate remain controlled by the same parties as during the past two years. 

Squabbling
And even for much of Tuesday, House approval of the fiscal legislation — which was negotiated by Senate Minority Leader Mitch McConnell, R-Ky., and Vice President Joe Biden — was far from certain. GOP leaders were forced to cajole conservatives who complained the fallback deal contained insufficient spending cuts. Only after it became clear that Republicans wouldn't have the votes to amend the Senate proposal — which the upper chamber said it wouldn't even consider — did House Speaker John Boehner, R-Ohio, bring the bill to the floor. 

The squabbling was familiar to any observers of Congress during the past two years. This divide almost resulted in a government shutdown and a default on the national debt in 2011. It again threatened Tuesday to allow the painful, across-the-board tax hikes and spending cuts to play out just as the U.S. economic recovery showed signs of accelerating.

PhotoBlog: See images of Congress working overtime to avoid fiscal cliff

And this deal just approved by Congress in the waning hours of 2013's first day all but ensures that much of the coming year will be dominated by similar battles in Washington. Republicans are hopeful they might be able to extract more spending cuts and entitlement reforms with the government up against other deadlines, like the one needed this spring to authorize more government borrowing. 

That could complicate Obama's already-ambitious second term agenda. The president said just this past Sunday on NBC's "Meet the Press" that he will seek comprehensive immigration reform legislation and new laws to address gun violence.

A group of hawkish Republican senators announced new legislation Wednesday to prevent billions of dollars of defense cuts called for after the supercommittee failed to reach agreement.

GOP Sens. Jon Kyl (AZ), John McCain (AZ), Lindsey Graham (SC) and Kelly Ayotte (NH) said this morning they will introduce legislation in January to keep the commitment to find $1.2 trillion more in government savings, but sparing defense funding in the meanwhile by looking to other parts of the government to slash spending.

"We will have a plan, we'll have it in January and I hope our colleagues would heed the words of our Secretary of Defense, of our service chiefs and every military expert that I know that cuts of this magnitude will put our nation's national security at risk," McCain said at a press conference on Capitol Hill.

Sen. Jon Kyl said it would be "impossible" to cut $600 billion from the Defense Department without harming national security.

"We wanted to make it clear what our intention is so that there is absolutely no doubt in anybody's mind that the across the board [cuts] to defense spending will not have to happen," Kyl said.

Whether the legislation advances is another story. And even if it did, President Obama has threatened to veto any attempt to undo the so-called "sequester" of cuts contained as part of the supercommittee agreement.

Sen. Graham called the idea of across-the-board defense cuts as the consequence of the super committee failure "ill-conceived". Sen. McCain called it "idiotic".

"It offends the hell out of me," Graham said, "these men and women have really gone out of their way to protect all of us."

"When you get Congressional leaders saying lets gut the military, put thousands of people at risk in terms of being kicked out. If you are going to fire anybody, fire us! And keep the soldiers," he said.

The senators said that the Defense Department is already planning for $450 billion cuts over the next ten years as a result of the debt ceiling deal and they could not absorb another $600 in cuts.

Where would they find the savings to replace the defense cuts? Kyl said there were savings identified by the supercommittee and by the Biden group that might go into the legislation. He said he was hoping this would be a bipartisan exercise.

Ayotte said, "We shouldn't subjugate our national security for our failure to do our jobs."