By a party line vote, a Senate panel has approved a ban on assault weapons, setting the legislation up for a vote next month in the full Senate.

But the bill’s prospects are not bright, as the ban – authored by California Sen. Dianne Feinstein – faces strong opposition from the National Rifle Association and other groups who say it infringes on Second Amendment rights.

The debate over the measure was marked by a fiery exchange between Feinstein -- who was the president of the San Francisco Board of Supervisors at the time of the assassination of openly gay city official Harvey Milk along with the city's mayor -- and freshman Sen. Ted Cruz of Texas.

Cruz, a former Texas solicitor general who has argued before the Supreme Court, asked Feinstein if she would consider limits to other amendments in the Bill of Rights, comparing her proposal to banning books protected by the First Amendment.

“I am not a sixth grader,” Feinstein replied. “Senator, I’ve been on this committee for 20 years. I was a mayor for nine years. I walked in, I saw people shot. I’ve looked at bodies that have been shot with these weapons.”

“It’s fine you want to lecture me on the Constitution,” she added. “I appreciate it. Just know I have been here for a long time.”

Feinstein said the legislation exempts over 2000 types of weapons. 

“Isn’t that enough for the people in the United States? Do they need a bazooka?” she asked. 

Cruz continued to press Feinstein for the answer to his question as other panel members tried to chime in.

“The answer is obvious,” an exasperated Feinstein replied. “No.”

The Senate Judiciary Committee approved a measure earlier this week to require all gun buyers to get a background check

Friday's school shooting in Connecticut prompted a renewed effort by lawmakers to re-evaluate gun rights, as a top Democrat vowed Sunday to introduce new legislation on the first day of the new Congress next year.

The massacre at an elementary school in Newtown, Conn. left 28 dead, including 20 students, seven adults and the suspected shooter, leading proponents of gun control to redouble their efforts to seek new regulations. New York City Mayor Michael Bloomberg, an outspoken advocate of gun control, said the issue should now be atop President Barack Obama's second term agenda.

To that end, California Sen. Dianne Feinstein, D, said she intended to introduce a gun control bill on the first day of the next Congress. Paired with a twin version in the House, Feinstein's law would take aim at limiting the sale, transfer and possession of assault weapons, along with the capacity of high-capacity magazines. 

"It can be done," she said on NBC's "Meet the Press." The senator, a proponent of gun control, said she expected Obama to offer his public support for the law. 

A federal ban on assault weapons, first passed in 1994 and signed by President Bill Clinton, expired in 2004. And while Obama has said he favors its reinstatement, the administration has hardly thrown its weight behind such a proposal during his first term. 

The especially grisly shooting in Connecticut — which follows several other high-profile shootings at a movie theater in Aurora, Colo., and outside a Sikh temple in Wisconsin — might now serve as a catalyzing moment in that dormant gun debate. 

"We're going to have to come together and take meaningful action to prevent more tragedies like this, regardless of the politics," Obama himself said on Friday in the aftermath of the Newtown shooting. 

Outspoken proponents of gun control, like Bloomberg, have now begun to pressure the president to speak out more forcefully on the issue. 

"It's time for the president to stand up and lead and tell this country what we should do," said the New York City mayor. "This should be his No. 1 agenda."

There are indications that some of the most commonly discussed measures to rein in weapons enjoy some degree of public support. An early August CNN/ORC poll, conducted in the aftermath of the Colorado and Wisconsin shootings, found varying levels of public support for different gun control proposals. Fifty-seven percent of adults, for instance, said they favored a ban on the manufacture, sale and possession of assault weapons, and 60 percent said they supported a ban on the possession of high-capacity ammunition clips. 

But gun owners' groups, like the National Rifle Association, could prove a significant political obstacle to moving any such proposals through Congress. The NRA — which endorsed Obama's Republican opponent, Mitt Romney, during the presidential campaign — remains a formidable political force. The group could target, for instance, Democrats from rural or centrist districts and states for defeat if they were to vote for such a law. 

Bloomberg argued otherwise. "There is this myth that the NRA is so powerful," he said. "Today the NRA's power is so vastly overrated."

In the meantime, the mayor said, Obama could take action through executive orders to strengthen and update the background check system and more aggressively enforce existing laws. 

On Sunday, the president will travel to Newtown to comfort victims' families and thank first responders for their efforts. Obama will also speak at a vigil this evening.