Republicans and Democrats vowed to push forward Tuesday with bipartisan efforts to reach a grand deficit-cutting deal even though President Barack Obama largely ignored the issue in his fiscal 2012 budget.

A growing coalition of Senators is working to bring the $4 trillion deficit reduction package proposed by Obama’s fiscal commission to the floor, said Sen. Mark Warner (D-Va.), who is leading the effort with Republican Sens. Saxby Chambliss (Ga.), Mike Crapo (Idaho) and Tom Coburn (Okla.), as well as Budget Chairman Kent Conrad (D-N.D.) and Majority Whip Dick Durbin (D-Ill.). Many more Senators support the idea.

“I think you guys are going to be surprised by the number of Senators who are engaged,” Warner said Tuesday.

Obama’s budget blueprint, released Monday, had some “good first steps,” he said,  but the bipartisan group is pushing for much more.

Conrad gave the president’s budget good marks, but only for the first year. The North Dakota Democrat said Obama failed to deal with the long-term challenges and warned of the risks to the country’s future unless a bipartisan debt deal is reached soon.

Conrad pleaded with White House budget director Jacob Lew for the administration to start providing guidance on how to bring together a deficit-slashing plan.

“Somehow, somewhere, we have got to find a way, and the administration has a big responsibility to [show] their vision of how this process comes together,” Conrad said. “We don’t have a lot of time. Sometime very soon there has got to be a negotiation” between House and Senate leaders and the White House, Conrad said. “The seriousness of that to the country can not be overstated.”

House Republican leaders and House Budget Chairman Paul Ryan (R-Wis.), meanwhile, released a joint statement vowing to put forward a budget plan of their own that takes on entitlement reform even as they prepare to pass a continuing resolution that contains $100 billion in midyear budget cuts to Obama’s 2011 budget request. Republicans have criticized Obama for failing to address entitlements in his 2012 budget proposal.

“Our budget will lead where the President has failed, and it will include real entitlement reforms so that we can have a conversation with the American people about the challenges we face and the need to chart a new path to prosperity,” they said in a joint statement.

And even though he didn’t tackle entitlements in his $3.7 trillion budget, Obama vowed Tuesday to push for a bipartisan deal on the issue.

At a news conference called to defend his budget, Obama accused his critics of being too impatient with him.

“This is not a matter of ‘You go first’ or ‘I go first,’” Obama said. “This is a matter of everybody having a serious conversation about where we want to go and then ultimately getting in that boat at the same time so it doesn’t tip over. And I think that can happen.”

Obama said Tuesday that his fiscal commission’s plan still provides a “framework” for negotiations, even though he didn’t put it in his budget and doesn’t support all of its recommendations. Obama’s budget cut $1.1 trillion in deficits over a decade — about a quarter of what the commission proposed.

Senate Minority Leader Mitch McConnell said there is still time to reach a deal, even though Obama missed an opportunity with his budget. “We are waiting for presidential leadership,” the Kentucky Republican said.

“I’ve been trying to get him to have that conversation for two years,” he said, adding that it doesn’t have to be in public.

Sen. Tom Carper, who is also pushing for a broad agreement, said he talked to the Democratic co-chairman of the fiscal commission, Erskine Bowles, about a week ago. “I told him this is a proposal that has legs, and I think time will prove me correct,” the Delaware Democrat said.

“The Senate in particular is very serious about responding to the challenge,” said Sen. Mark Udall (D-Colo.), who also supports the commission blueprint. “It spreads the pain equally.”

But hanging over the debate are the 2012 elections, and both parties are worried that the other will use specific proposals against them.

The attacks are already starting, with Senate Democratic Conference Vice Chairman Charles Schumer warning GOP leaders.

“If Paul Ryan’s Roadmap is any indication, the House Republicans’ idea of entitlement reform will be privatizing Social Security and turning Medicare into a voucher system,” the New York lawmaker said in a statement. “Any such plans will be dead on arrival in the Senate. Democrats will fight any attempt to break our promise to America’s seniors. We want to extend the life of Social Security and eliminate waste in Medicare, but we will not go along with proposals that seek to end these programs.”

Obama, meanwhile, tried to sound hopeful about the prospects for a broad agreement between the warring sides, noting that he successfully worked with Republicans on tax cuts in the lame-duck session. There is an impatience in Washington, D.C., when things don’t happen immediately, he said.

“My goal here is to actually solve the problem. It’s not to get a good headline on the first day,” Obama said.

But talking about cutting the deficit is a lot easier than actually doing something about it; indeed, a parade of Republican and Democratic Senators have been pushing for budget caps, constitutional amendments and other mechanisms first rather than lead with their chins on painful cuts to Social Security or Medicare.

“I think a lot of people talk about what they want to cut, but they get very nervous when they get to the specifics,” Sen. Patrick Leahy (D-Vt.) said.