Phil Kerpen, a vice president at Americans for Prosperity, an organization that promotes free market policies that has worked with Tea Party groups around the country, said that he believes new members elected on a wave of sentiment against big government will be more skeptical of the military’s budget, which has climbed steadily since 1998 and has nearly doubled since 2000, to $675 billion this year.

“I said, ‘We need a liberal and conservative coalition, an intellectually honest approach to this,’ ’’ Frank recalled. “I said ‘Do you want to work together on this?’ And he said ‘Of course I do.’ ’’

Chris Preble, director of foreign policy studies at the libertarian Cato Institute, helped bring Frank and Paul together on the issue. He wrote an article earlier this year in which he called for significant defense cuts. Frank read the article and sent it to Ron Paul, with whom he had worked previously on attempts to decriminalize marijuana use and online gambling.

“If you want to be serious about cutting the federal budget, we have to look at the Pentagon budget,’’ said Justin Amash, a newly elected libertarian-leaning Republican House member from Michigan who said he admires Ron Paul and met with him Tuesday.

Many Republicans have traditionally demanded that military spending — which accounts for about 23 percent of the federal budget — be off-limits even as the deficit grew. But the alliance between Frank and Paul, the father of Rand Paul, a Tea Party flag-bearer who was just elected senator from Kentucky, comes at a time when some newly elected Republicans view soaring military spending as part of the deficit problem.

“We incorporated a good bit of it,’’ said Alan K. Simpson, the former Republican senator from Wyoming who cochairs the debt commission, in a telephone interview. “If I read another article that tells me we can get this whole thing settled without touching Social Security, Medicaid, or the Pentagon, I’ll barf.’’

A growing number of Republicans are saying that Pentagon cuts should be considered. And earlier this month, the White House debt commission issued draft recommendations that contained some ideas from a study commissioned by Frank and Paul, including dramatic reductions in the size of US military bases in Europe and canceling some big-ticket weapons systems.

Initially, their proposed 16 percent cut over a decade got a cold reception on Capitol Hill, where many Democrats and even the most fiscally conservative Republicans view the Pentagon budget as basically off-limits. But now, with talk of deep cuts in Social Security and Medicare, and as a Tea Party-infused strain of the Republican party grows more powerful, their views are gaining traction.

WASHINGTON — Earlier this year, Representatives Barney Frank, the unabashedly liberal Democrat from Newton, and Ron Paul, an outspoken libertarian Republican from Texas, formed an unlikely alliance aimed at slashing the defense budget to trim the deficit.

Rand Paul is among the newly elected Republicans who say cuts to the Pentagon’s budget should be considered. Although he is not as outspoken as his father on the matter, the senator-elect has called for an end to “nation-building’’ and downsizing the US military’s responsibilities in Europe, East Asia, and Afghanistan.

“National defense is the most important thing we do in Washington, but there’s still waste in the military budget,’’ Rand Paul told ABC’s “This Week’’ earlier this month. “You have to make it smaller. But you also then need to address how many wars are we going to be involved in? Are we going to be involved in every war all the time?’’

These sentiments have alarmed some veterans in Congress on both sides of the aisle, who fear a budding coalition between the far right and the far left aimed at curtailing US military power around the world.

Last Monday, Arizona Senator John McCain, a Republican, told a foreign policy forum that he worries “a lot about the rise of protectionism and isolationism in the Republican Party,’’ citing Rand Paul’s remarks.

Senator Joseph Lieberman, the Connecticut independent, warned in an op-ed piece in The Wall Street Journal that a coalition of antiwar Democrats and isolationist Republicans would present “the single greatest political threat to the success of the war effort in Afghanistan.’’

It remains unclear how many of the new freshmen will ally themselves with the libertarian wing of the GOP. Even Frank and Ron Paul say it will be an uphill battle to gain support for large defense cuts.

“Even with new people coming in, the likelihood of us getting ahold of this budget problem is small,’’ said Ron Paul in an interview. He said that he and his son have not discussed the issue.

Frank and Ron Paul began working together on the matter earlier this year, after President Obama announced a three-year spending freeze across the federal government but exempted the Pentagon, Medicare, Medicaid, and Social Security.

Defense Secretary Robert Gates has said he can eke out savings of about 2 percent of the Pentagon budget each year, but he has argued the Pentagon should keep that money for other priorities, and that its budget should still grow at a rate of about 1 percent a year.

To offer specifics on how defense spending can be trimmed, Frank and Paul set up what they called the Sustainable Defense Task Force, a group of specialists led by the Project on Defense Alternatives, a Cambridge, Mass.-based think tank focused on reducing military spending.

The task force released a report in June that identified about $1 trillion in cuts over the next decade out of a projected $6 trillion in spending during that period. It called for cutting expensive weapons systems with a history of problems, including the F-35 Joint Strike Fighter, the Expeditionary Fighting Vehicle, and the Osprey aircraft, and for a 26 percent reduction in personnel at US military bases in Europe and Asia.

“If England and Germany feel threatened, they can increase their own militaries,’’ said Frank, who noted that both European allies are cutting their own defense budgets.

Frank and Ron Paul also circulated a letter to the White House debt commission urging it to consider military cuts. Of 57 lawmakers who signed, Ron Paul was the only Republican.

But since then, others have shown more interest.

Senator Tom Coburn, a conservative Oklahoma Republican who sits on the debt commission, has proposed freezing military spending until the Pentagon is audited. A draft recommendation from the cochairmen of the commission called for reducing the number of US service members in Europe and Asia by a third, and axing expensive weapons systems singled out by the Frank-Paul task force.

But some of their recommendations were dead on arrival. For instance, the task force suggested curbing the planned modernization of the US nuclear arsenal, but the Obama administration is reportedly planning to add $4 billion to such efforts in an attempt to gain the support of Senator Jon Kyl, an Arizona Republican who advocates boosting the nuclear arsenal, for a key arms treaty with Russia.

Nonetheless, Erskine B. Bowles, the Democratic cochair of the debt commission, said he is hopeful that some military cuts will be accepted. He credited Frank and Paul with helping to spark a useful debate in the country.

“Everything changes as people become more aware,’’ he said. “What was possible three weeks ago is different than what is possible today, and what will be possible two weeks from now.’’

Farah Stockman can be reached at fstockman@globe.com.

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