Over the next few weeks, Republicans will begin the painful self-examination that follows electoral defeat. That process is likely to reveal new schisms in the party on domestic issues like immigration and possibly even gay marriage. But in Congress, the last redoubt of the party’s national power, a fight is brewing over foreign policy as well.

During the 2012 campaign, it was often difficult to figure out where Republicans stood on foreign policy. Romney got national-security advice from neocons like Eric Edelman (a former top Cheney aide) and Dan Senor—but he also tasked Robert Zoellick, a bête noir of neocons who is generally associated with the realist (i.e., less interventionist) wing of the GOP, with leading his national-security transition. Romney himself sounded contradictory notes. He sometimes employed tough rhetoric in discussing Russia and China. Yet during the third and final debate—which focused on national security—he often sounded indistinguishable from Obama.

But the coming intra-Republican debate won’t pit realists against neocons so much as it will pit both groups against the Tea Party. While neocons and realists may differ on how frequently and where America should deploy its power, they are generally in agreement that America should have a military befitting a superpower.

This is not, however, the case for many (though not all) Tea Partiers. As Dean Clancy, the legislative counsel for Freedom Works, an advocacy group closely aligned with the Tea Party, told The Daily Beast, “We think defense should contribute its fair share toward balancing the budget over the next 10 years.” In other words, the military, like the welfare state, needs to be cut.

In the coming weeks, the defense budget will be at the center of negotiations over the deficit. If no compromise is reached before January, there are supposed to be sharp reductions in defense spending over the next 10 years totaling around $500 billion—part of a process known as sequestration. “Our No. 1 concern is that Congress not call the whole sequester off,” Clancy said.

John Hart, the communications director for Oklahoma Republican Sen. Tom Coburn, put it this way: “For Republicans, defense has been our Medicare, a sacrosanct area of the budget that shall not be cut.” Hart said that his office will be releasing a new report next week that will identify $60 to $70 billion in what it calls “non-defense defense spending,” just in time for budget negotiations. “The only way both sides will come together is if both sides put everything on the table,” Hart said. “We will continue to make this case to those in our own party.”

The other side of this debate also recognizes that a philosophical fight could be around the corner. Jamie Fly, the executive director of the Foreign Policy Initiative, a conservative think tank founded by Weekly Standard editor William Kristol initially to support a troop surge in Afghanistan, said he anticipates intraparty arguments about military spending. “There are likely to be continued debates within the right about how to respond to [Obama’s] drawdown in Afghanistan, how to avoid defense cuts without raising taxes, and what the appropriate response is to crises such as Syria,” Fly said.

As this debate unfolds, there may be some areas where out-of-power defense hawks could triangulate with President Obama in order to save the defense budget or argue against a precipitous retreat from the world stage. Of course, whether Obama is willing to work with these Republicans will depend on many things: among them, how hard House Republicans press his administration on the assault in Benghazi that killed Ambassador Chris Stevens and three other Americans.

When the Republicans are out of power, the party of Lincoln tends to embrace its more isolationist strain. (Think of former House Majority Whip Tom DeLay opposing Bill Clinton’s intervention in Serbia during the 1990s.) Now, with the rise of the Tea Party and with defense spending about to take center stage in Washington, that strain could be more prominent than ever. Which means that, on foreign policy as on many other subjects, Republicans have a lot of internal arguing ahead of them.