The package of legislative measures meant to stem gun violence - proposed by President Barack Obama last week -- was met with varying forecasts of success Sunday by lawmakers who will take up the plan in the coming days.
And David Plouffe, a senior adviser to Obama, told CNN's chief political correspondent Candy Crowley that he was confident certain measures, like reinforcing laws mandating background checks during gun sales, would succeed in Congress.
"There are 60 votes in the Senate and 218 votes in the House, if votes will come up for some of these gun safety measures, like gun clips, like universal background checks," Plouffe said on "State of the Union." "There's a consensus in America on this and I think we can get here on Capitol Hill."
On Wednesday, Obama signed 23 executive actions -- which don't require congressional approval -- to strengthen existing gun laws and take related steps on mental health and school safety.
He also called on Congress to reinstate an assault weapons ban that expired in 2004, to restrict ammunition magazines to no more than 10 rounds, and to expand background checks to anyone buying a gun, whether at a store or in a private sale at an auction or gun show.
Sen. Chuck Schumer, the number three Democrat in the Senate, said a bill on background checks was imminent in the upper chamber.
"I think you're going to see a very good likelihood in the next week or two a proposal that has broad support for universal background checks," the New York Democrat said on NBC's "Meet the Press."
"This is the best chance of getting something done, and I think you're going to find much broader support than we've ever imagined," he added.
His Republican colleagues sounded less confident. Sen. John Barrasso, R-Wyoming, said on "State of the Union" he didn't think 60 votes on a background check measure or a ban on high capacity gun magazines was likely - and that certain Democrats could be to blame.
"I don't think that [Senate Majority Leader] Harry Reid even brings it to the Senate floor because he has six Democrats up for election in two years in states were the president received fewer than 42% of the votes," Barrasso said. "He doesn't want his Democrats to have to choose between their own constituents and the president's positions."
Those six vulnerable Democrats - Max Baucus of Montana, Mark Begich of Alaska, Tim Johnson of South Dakota, Mary Landrieu of Louisiana, Kay Hagan of North Carolina and Mark Pryor of Arkansas - have not yet indicated where they stand on the measures Obama is pressing. But Reid indicated in a statement after the plan was released that he was "committed to ensuring that the Senate will consider legislation that addresses gun violence and other aspects of violence in our society early this year."
On "Meet the Press," Sen. Ted Cruz, a newly elected Republican from Texas, asserted Obama was taking advantage of the Newtown tragedy to promote a liberal agenda.
"The president began trying to exploit that tragedy to push a gun control agenda that is designed to appeal to partisans, designed to appeal to his political partisans," Cruz claimed.