Despite the political and economic risks, congressional Republicans are forging ahead with proposals for severe budget cuts, even though party leaders acknowledged the reductions could lead to job losses in the name of deficit reduction.

Criticism mounted at the start of a House debate as Democrats took aim at GOP plans to maintain tax breaks for oil companies and the wealthy while cutting medical research, community policing and funding for “Sesame Street” as a “mindless” exercise that would do little to address the nation’s $1.5 trillion deficit.

The sheer depth of the cuts has prompted concern among hometown mayors and local law enforcement officials. Still, GOP leaders said the rollback is necessary, even at the expense of thousands of jobs funded by government programs on the chopping block.

“If some of those jobs are lost in this, so be it,” said House Speaker John Boehner, R-Ohio. “We’re broke.”

President Obama vowed Tuesday to veto the spending plan in the unlikely event it passed the Democratic-controlled Senate, and questioned proposals such as one to limit formula to infants.

“Is that who we are as a people?” Obama asked at a news conference. “I think the American people may conclude, you know, let’s have a more balanced approach.”

Republicans compiled a thick set of proposed cuts last week, but it was rejected by the most conservative House members. Leaders amassed a new set of cuts that would reduce 2011 spending by about $61 billion.

The cuts are concentrated in less than 15 percent of the federal budget, the portion that funds so-called nondefense, discretionary spending including education, health, environmental protection and child services.

As the debate plays out this week, both the Republicans and the White House are vying for approval from independent voters, who flocked to the president in the 2008 election but have since drifted to Republicans.

The nation’s record $1.5 trillion deficit has animated voters, and Republican strategists said their internal polling gives them confidence that voters who are unaligned with either party will support their proposed cuts.

But Republicans also take the risk that the cuts will appear extreme, and GOP strategists privately worry about the tenuous link between spending cuts and voter concerns over job growth.

Obama unveiled his 2012 blueprint earlier this week with a nod to unaligned voters. He proposed trimming community programs supported by his liberal base while funding programs intended to spur education and economic growth.

The liberal-leaning Economic Policy Institute has estimated as many as 800,000 jobs could be lost under the Republican proposal.

Still, lawmakers heavily supported by tea party voters appeared ready Tuesday to double-down on the political strategy, amid an ever-shifting national mood.

The cuts are part of a measure to continue funding the government beyond March 4, when the existing spending plan expires. Without approval of a new spending plan, the government faces the possibility of a shutdown.

But even beyond the cuts in the spending plan, Republicans are insisting on many others. More than 400 amendments were filed by lawmakers at the start of the House debate, many seeking further reductions to government operations through Sept. 30.

The GOP reluctance to cut Pentagon spending became apparent as voting began when an amendment to cut $18 million in Defense Department operations and maintenance was rejected.

Still, Boehner has promised the cuts in the final House bill will be even steeper than the $61 billion outlined, an unsettling prospect to some lawmakers.

“Nobody told me it would be easy coming here,” said Rep. Michael Fitzpatrick, R-Pa., who won back the politically divided district he lost to a Democrat four years ago.

Along with amendments to defund Obama’s health care law, Republicans want to end the administration’s home mortgage refinancing program and halt funding for the administration’s suit against Arizona’s anti-illegal immigration law. Lawmakers also would zero out $2 million set aside for restoration and repairs at the White House.

Freshman Rep. Tim Huelskamp, R-Kan., said that at the 14 town hall meetings he conducted earlier this month in his district, a Republican stronghold, he was most frequently asked why he couldn’t cut more.

In the Senate, Republican Leader Mitch McConnell of Kentucky suggested that Democrats, not Republicans, should re-evaluate their stance.

“I know there’s probably a perception in this town that it’s politically hazardous to reduce government spending in a dramatic way,” McConnell said. But some elected officials enjoyed rising approval ratings as they cut spending in their states, he said.

“I would encourage our friends on the other side of the aisle, 23 of whom are up in ’12, to take another look at where they think the politics of this all might be,” McConnell said.

Yet in a nod to home-state constituencies, some Republicans were filing complicated amendments that would eliminate funds in one place but reinstate them in another.

As the debate got under way, five-term Rep. Rob Bishop, R-Utah, was headed to a meeting with a judge, certain he was about to receive an earful over the proposed elimination of federal funds to hire local police officers.

But he was interested in making steeper cuts and confident of the promised reductions. Then again, things could change by the time final votes take place this week.

“When everyone’s tired and cranky,” he said, “who knows what will happen?”