Republicans on the House Budget Committee are talking about increasing defense spending beyond President Trump's proposed $54 billion boost, which has led to an impasse between defense hawks and deficit hawks.

The fight has forced the committee to postpone the rollout of its 2018 budget resolution, a key element in moving Trump's legislative agenda forward.

The House GOP may have the opportunity to settle on a strategy when it meets for its weekly policy discussion this Wednesday, a meeting that will focus on budget and appropriations.

A House GOP aide with knowledge of the process said it would be "a very strong possibility" that the defense cap proposed in the House budget resolution would be higher than Trump's request of $603 billion for the next fiscal year.

In his budget proposal, Trump cut $54 billion from from nondefense discretionary spending to pay for the new defense spending.

Defense hawks such as Sen. John McCain (R-Ariz.) and House Armed Services Committee Chairman Mac Thornberry (R-Texas) want to go further. They have called for $640 billion in defense spending.

Rep. Tom Cole (R-Okla.), a House Budget Committee member close to GOP leadership, thinks there's a good chance the number will be bigger than Trump's request.

"I think the defense number could easily be more, because we have a lot of folks that think we could go further," he said.

Members of the conservative House Freedom Caucus, however, bristle at the idea of spending an additional $37 billion on defense - and potential increases to non-defense spending -without finding additional cuts elsewhere.

"Conservatives are willing to entertain the idea of voting for higher spending levels on discretionary spending if we can get the right kind of reconciliation instructions," said Rep. Jim Jordan (R-Ohio), a Freedom Caucus member.

The reconciliation instructions in question would mandate that congressional committees achieve certain spending cuts, a vehicle to push for deeper reforms.

Those reforms, Jordan said, would be enough of an achievement to persuade Freedom Caucus members to swallow increases on both defense and nondefense discretionary spending, even if they increase the deficit in the short run.

"Either that, or leadership can do what they've done the last six years, which is wait until Sept. 30 at 11:59 p.m. and negotiate a bad deal," he said.

During his campaign, Trump promised not to allow cuts to Medicare or Social Security, entitlement programs that congressional Republicans see as major sources of potential savings. Tax hikes would violate a pledge signed by almost every House Republican not to create new taxes.

The remaining sources of spending, welfare programs such as Supplemental Nutrition Assistance Program, commonly known as food stamps, and Temporary Assistance for Needy Families, were already slashed in Trump's proposal, making more savings painful and difficult to find.

The Budget Committee had set its sights on unveiling the resolution this week, but may now delay it until next week or even after the Fourth of July recess, which could gum up the tight legislative agenda.

Without a budget resolution in place, appropriators cannot go about the business of doling out spending authority to the government. Congress must pass its spending bills by the end of September if they want to avoid a government shutdown.

Alternatively, Congress could pass a continuing resolution to keep the government funded at 2017 levels, but that would preclude any defense increases, as well as spending authority for Trump's other priorities, such as building a border wall.

On top of all that, without a budget resolution conferenced between the House and Senate, Republicans will not be able to put in place a special procedure that circumvents the Senate filibuster, which they will need in order to pass tax reform.

House Minority Leader Nancy Pelosi (D-Calif.) slammed her Republicans colleagues for failing to produce a budget resolution

"Almost five months into the Trump administration, House Republicans still haven't met their most basic responsibility to pass a budget," Pelosi said.

"The House GOP is now months behind the statutory budget deadline, deeply divided but unwilling to abandon their budget giveaways to the richest few."

Updated at 7:32 p.m.