As President Obama prepares to meet Monday with Senate leaders to try to restart talks about the swollen national debt, some Republicans see a potential path to compromise: significant cuts in military spending.

Senior GOP lawmakers and leadership aides said it would be far easier to build support for a debt-reduction package that cuts the Pentagon budget — a key Democratic demand — than one that raises revenue by tinkering with the tax code. Last week, Republicans walked out of talks led by Vice President Biden, insisting that the White House take tax increases off the table.

In listening sessions with their rank and file, House Republican leaders said they have found a surprising willingness to consider defense cuts that would have been unthinkable five years ago, when they last controlled the House. While the sessions have sparked heated debate on many issues, Rep. Peter Roskam (Ill.), the deputy GOP whip, said there are few lawmakers left who view the Pentagon budget as sacrosanct.

“When we say everything is on the table, that’s what we mean,” said House Majority Whip Kevin McCarthy (R-Calif.), the No. 3 leader who has been hosting the listening sessions in his Capitol offices.

Freshman Rep. Adam Kinzinger (R-Ill.) could serve as a poster boy for the new breed of conservatives who are eager to wipe out government waste and inefficiency, no matter where they find it. Kinzinger, an active-duty Air National Guardsman who flew missions in Iraq, fought successfully last month to cut a request for $100 million to buy new flight suits for Air Force pilots. The old ones, he argued, are good enough.

Defense spending is “a pillar of Republican strength. It’s a pillar of national strength. Look, I know there are sacred cows,” Kinzinger said in an interview. “But we cannot afford them anymore.”

With the clock ticking toward an Aug. 2 deadline to raise the legal limit on federal borrowing, defense spending has been a major stumbling block in negotiations between the two parties. While both sides view the tax issue as the biggest hurdle, negotiators spent much of their final three-hour session arguing over agency spending before Republicans declared an impasse last Thursday, according to people familiar with the talks.

The White House has offered nearly $1 trillion in cuts to domestic agencies over the next decade and $300 billion more from security agencies. But House Majority Leader Eric Cantor (R-Va.) pressed for as much as $1.7 trillion in cuts. And he wanted an overall cap on spending that would leave the door open to slashing the entire sum from domestic programs — such as education, food safety, health research and criminal justice — when lawmakers draft spending bills next spring.

“Everything is on the table,” Cantor said in an interview afterward. But the decision on how much to cut defense “belongs in the appropriations process.”

White House budget director Jack Lew objected, and the meeting grew heated. Democrats said they could never support a package that targets only social programs and extracts no pain from the military, big business or the wealthy.

“To get anything through the House, you’re going to need some Democratic votes. This isn’t a one-way street here,” said a senior administration official, speaking on the condition of anonymity to discuss the closed-door sessions. “It’s clear that any package is going to have to have significant spending reductions, including in Pentagon spending.”

The official said the package must also “have some of these tax deductions closed,” referring to perks in the tax code that benefit the oil and gas industry, hedge fund managers and jet-setting corporate executives. But if Republicans agree to significant Pentagon cuts, the White House may find it easier to accept a deal that includes less in new revenue, people familiar with the talks said.

The GOP has not been entirely closed to tax changes, according to people in both parties. They mentioned a proposal to adjust the way business inventory is taxed, which could generate as much as $70 billion over the next decade, as one potential area of compromise. An additional $6 billion a year could be generated by wiping out subsidies for ethanol blenders. A similar proposal passed the Senate two weeks ago with overwhelming Republican support.

The White House may be more interested in such a deal than congressional Democrats, who have been adamant about raising taxes on the wealthy. “Make no mistake, there needs to be revenues in any deal,” Sen. Charles Schumer (D-N.Y.) said in a conference call with reporters Friday. “Republicans cannot insist on protecting tax breaks for millionaires at the expense of our economy.”

Still, some Democrats said they place a higher priority on defense cuts.

“Defense spending is damaging spending. Many of us believe it does more harm than good to our people and to our reputation in the world,” said Rep. Barney Frank (D-Mass.). “If we can get $100 billion from reducing unneeded military spending, that’s better than $100 billion in taxation.”

Getting to an agreement to cut defense spending may not be easy, however. Many Republicans are still hawkish and want to fully support U.S. troops abroad. Rank-and-file lawmakers said they specifically oppose any across-the-board reductions to the Pentagon budget, preferring that incoming Defense Secretary Leon Panetta present Congress with a detailed plan of programs to be slashed.

Outgoing Defense Secretary Robert M. Gates has advocated for some cuts, especially related to costly new military hardware, but has warned of the consequences of deep or across-the-board reductions that could jeopardize U.S. military strength in the future.

“Our caucus would come in and say, ‘This is a reasonable place for defense,’ as long it wasn’t arbitrary and capricious. If the secretary reworked the numbers, our guys would go, okay,” said a senior GOP aide, who said the White House has so far refused to offer a detailed annual spending plan for the Pentagon. Without official guidance, the aide said, “it’s kind of like: Pick the defense number. And we can’t do that.”

Senate Minority Leader Mitch McConnell (R-Ky.), a critical player in the talks, has taken the same position as Cantor — that congressional appropriators should decide where to cut spending. McConnell, a senior member of the Appropriations Committee who touted his ability to deliver defense dollars to his state in his 2008 reelection campaign, is part of a powerful Republican old guard that has fought for years to expand military spending, as much to benefit constituents as for reasons of political principle.

Today, however, the old GOP hawks are finding that their tea-party-influenced troops are more interested in saving money than protecting turf at the Pentagon. Rep. Tim Scott (R-S.C.), a leader among the 87 House Republican freshmen, said the military budget is widely viewed as loaded with pork that has little bearing on the day-to-day battles in Afghanistan and other hot spots.

“If there are sacred cows, we ought to find them and get rid of them,” said Scott, who represents a district where more than a third of voters hail from military families.

“I would never support anything that would reduce the safety of the troops on the ground,” said Rep. Robert Hurt (R-Va.), a freshman whose district runs south from Charlottesville. “But bureaucracy is bureaucracy, and there are ways to get at it, even in the Pentagon.”