WASHINGTON >> At a news conference to showcase how Republicans will handle their looming debt ceiling showdown with Democrats, Sen. Ron Johnson of Wisconsin was asked to explain what specific spending cuts his party would support in exchange for lifting the borrowing cap.

“Exactly what those are, we’re not willing to lay out here today,” Johnson said in January, adding that plans would be determined in consultation with House Republicans.

The refrain has been familiar in recent weeks as Republicans have insisted that they want “structural” fiscal changes in exchange for voting to raise the borrowing cap, but they have so far declined to offer a cohesive plan outlining what programs they would cut. Internal divisions over how to reduce spending have been spilling into public view, underscoring the political challenge that Republicans face as they try to wield the specter of a default to extract concessions from President Joe Biden and Democrats.

In the meantime, the United States technically has already exceeded the $31.4 trillion debt limit, and the Treasury Department has warned that its ability to delay a default by using its so-called extraordinary measures could be exhausted by early June.

Today, Biden will meet with Speaker Kevin McCarthy at the White House to discuss the debt limit and budget priorities. Before that meeting, White House officials said, Biden will ask the Republican lawmaker to commit to the principle that the United States will never default on its financial obligations and press McCarthy about when House Republicans plan to release their budget.

“It is essential that Speaker McCarthy likewise commit to releasing a budget, so that the American people can see how House Republicans plan to reduce the deficit.” Brian Deese, director of the White House’s National Economic Council, and Shalanda Young, director of the White House budget office, wrote in a memo released Tuesday.

McCarthy accused Biden on Tuesday of being irresponsible by suggesting that he was unwilling to seek common ground over the debt ceiling and said that the White House’s refusal to bargain was “childish.”

“Why would you put the economics of America in jeopardy?” McCarthy said to reporters. “Why would you play political games? I’m not.”

But reaching a deal will not be easy. The White House has said it will not negotiate over raising the debt limit, and Republicans have been struggling to find agreement among themselves over how to cut spending. Deficit reduction pledges are poised to collide with the reality that austerity measures tend to be unpleasant.

“The public doesn’t like debt and deficits, but it doesn’t like spending cuts or tax increases, either,” said William G. Gale, a senior fellow at the Brookings Institution and the author of “Fiscal Therapy: Curing America’s Debt Addiction and Investing in the Future.” “Against that backdrop, why would any politician fall on his sword to cut spending or raise taxes?”

After a $5 trillion spending spree to combat the coronavirus pandemic, the nation’s debt burden has become too enormous to chip away at without considerable pain. The Committee for a Responsible Federal Budget estimated that it would require $14.6 trillion in deficit reduction to balance the budget over the next decade. That feat would require all spending to be cut by roughly one-quarter.

Excluding the most politically crucial budget items — defense, veterans, Social Security and Medicare — would require an even bigger scalpel. With those off the table, spending the remaining “discretionary” items would need to be slashed by 85%.

For months before the midterm elections in November, Biden warned voters that if Republicans won control of Congress, they would seek to slash funding for social safety net programs, threatening Social Security and Medicare. That has left Republicans on the defensive since taking control of the House this year, as making a dent in future deficits is practically impossible without touching those programs.

Many Republicans are mindful that they are facing something of a political live wire. Former President Donald Trump warned Republicans to steer clear of the retirement programs during the debt ceiling negotiations. “Under no circumstances should Republicans vote to cut a single penny from Medicare or Social Security,” he said in a video message in January.

Despite vague proposals to restructure the safety net programs, most Republicans insist they merely want to cut waste from the programs to preserve them for the long term.

The White House and Republicans are expected to unveil detailed budget proposals over the next two months that will formally lay out spending priorities. The Biden administration’s budget will be released March 9. Rep. Steve Scalise of Louisiana, the majority leader, suggested Tuesday that House Republicans would submit a budget in April.

“I hope the president meets his deadline, just like we’re going to work to meet our deadline,” Scalise said at a news conference.

The contours of that budget are starting to take shape, but differences within the Republican Party will not be easy to bridge.

Rep. Chip Roy, R-Texas, who withheld support from McCarthy in his run for House speaker, said McCarthy had committed to enact the biggest discretionary spending cuts in history for the upcoming fiscal year. He said that a $130 billion reduction could be accomplished without cuts to military spending, Social Security or Medicare. Instead, he said on Twitter, money that goes to “woke & weaponized bureaucrats” would be scaled back.

But other influential Republicans contend that big changes to so-called entitlement programs must be considered.

Rep. Matt Gaetz, R-Fla., said on Fox News last week that he was disappointed that some of his colleagues had given up on overhauling safety net programs such as Medicaid and the Supplemental Nutrition Assistance Program, which provides food stamps. He called for changes that would make fewer people eligible to receive the benefits.

“If we impose work requirements on SNAP and on Medicaid expansion for able-bodied adults, we would have the ability to save $1 trillion during the 10-year budget window,” Gaetz said.

Some Republicans, such as Sen. Rand Paul of Kentucky and Rep. Nancy Mace of South Carolina, have been calling for “penny plans” that would cut total spending across the board by a percentage to balance the budget in as little as five years.

Russell Vought, Trump’s director of the Office of Management and Budget, has produced the most detailed budget proposal thus far. He has been talking with House Republicans since late last year about how to balance the budget without making cuts to Social Security and Medicare.

The plan includes a $22 billion cut to the Department of Health and Human Services that would gut funding for the Centers for Disease Control and Prevention and cut $26 billion from the Department of Housing and Urban Development, including a phaseout of Section 8 grants that Vought says are “a magnet for crime and decreased property values.” It would also freeze Medicaid, eliminate the Affordable Care Act’s coverage expansions and reduce disability benefits for veterans.

Biden and his aides have increasingly called for House Republicans to make their debt-limit demands clear, as proposals that would reduce funding for the poor and for veterans could prove to be a political gift for the president.

However, the White House has held firm that Biden does not intend to cut a deal to raise the debt limit and warned that Republicans were being reckless by threatening the full faith and credit of the United States.

“Raising the debt ceiling is not a negotiation,” Deese and Young wrote in their memo Tuesday.