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Obama hits Capitol Hill -- and a few snags along the way

President Barack Obama huddled with Senate Democrats on Capitol Hill Tuesday, stepping onto congressional turf as part of a week of outreach to both his own party and his GOP rivals.

With new budget and gun control bills snaking through the legislative process -- and with comprehensive immigration reform measures being drafted by bipartisan lawmakers -- Obama’s series of in-person conversations with congressional heavies are meant to smooth the way for compromise after the budget sequester stalemate last month.  

But it’s not exactly a bipartisan campfire kumbaya.

Even as the president was leaving the building, Senate Majority Leader Harry Reid told reporters that Oklahoma Republican Sen. Tom Coburn has already said he will object to a bipartisan measure to temporarily fund the federal government -- a snag that could slow efforts to avert a government shutdown later this month.

Jacquelyn Martin / Jacquelyn Martin / AP

Sen. Tom Coburn, R-Okla. walks toward the Senate chamber on Capitol Hill in Washington, Monday, Dec. 31, 2012.

“This is in this new era of ‘let’s get along,’ all this cheering and yelling about this ‘bipartisan’ bill,” Reid lamented to reporters after meeting with Obama, “I just learned when I was in here with the president that -- who else? -- Coburn now won’t let us move the bill.”

And the news of that hiccup wasn’t the only challenge Obama received during his trek to Capitol Hill.

One Democrat in the room told NBC News that a senior senator in the closed-door meeting challenged the president on his administration’s unmanned drone policy, saying the White House has treated Obama’s own party poorly in dealing with the issue.

The meeting with Senate Democrats -- which participants said included discussion of entitlement reform, immigration and gun control -- kicked off a series of closed-door sessions that Obama has scheduled this week with lawmakers on the other end of Pennsylvania Ave, including a Wednesday luncheon with House Republicans.

His conspicuous “charm offensive” aimed at the GOP started last week, when he dined with a dozen Republican senators as well as with House budget chief Rep. Paul Ryan.

For the most part, Republicans say ‘the more, the better’ when it comes to Obama’s outreach.  

“We welcome it,” Senate Minority Leader Mitch McConnell told reporters on Capitol Hill Tuesday.

Senate Majority Leader Harry Reid reacts to the fiscal plan unveiled Tuesday by Rep. Paul Ryan.

“It’s a good opportunity to have a candid conversation and we all know that, with the president’s request to raise the debt ceiling here again later this summer, we will be discussing again the possibility of finally solving our huge deficit and debt problems by making the kind of changes to [entitlements] that we all know we have to make to save these programs and save our country,” McConnell said.

Still, the effort has not been without some skeptics.

A National Journal report out Tuesday morning quoted an unnamed White House aide griping that the vigorous schedule of bipartisan meetings is “a joke” and a waste of time staged merely to make the press “happy.”

White House spokesman Jay Carney dismissed that sentiment as inaccurate during a briefing with reporters.

“I have no idea who said that," he said. "But I can tell you that opinion has never been voiced in my presence, in the president's presence, in the West Wing. It does not represent the president's view, it does not represent the White House's view, and it does not represent the administration's view."