Senate Republicans are coalescing around a push to raise discretionary spending caps and suspend the statutory debt ceiling for two years, rather than the one-year stopgap plan pushed by White House officials, according to the chamber’s No. 2 Republican.

“I think they believe that it would be good to deal with both of those issues for not just this next year, but for the following year as well,” said Majority Whip John Thune, R-S.D. “I suspect there are others who maybe don’t share that view, but I think the overwhelming majority of the Republicans, I think that’s what they believe.”

That view likely puts the onus on Republicans to come up with a unified position among senators, House lawmakers and the White House. Thus far House Democrats have been digging in their heels on the fiscal 2020 levels that chamber has already been moving through the legislative process.

Bipartisan discussions have mostly broken off, though House Speaker Nancy Pelosi, D-Calif., has been speaking with Treasury Secretary Steven Mnuchin by phone, including another scheduled call on Thursday. Pelosi wants to ensure that spending caps are raised to some acceptable level as part of any package dealing with the debt limit, or they might lose leverage later this year in talks with the White House.

Pelosi on Thursday declined to commit to passing legislation addressing the debt limit before the August recess. But she said she also doesn’t want there to be “any doubt about the full faith and credit of the United States.”

“We’ll just see about the timing. We’re having our back-and-forth conversations,” Pelosi said. “We also understand how important it is for us to lift the caps, so that we can meet the needs of the American people. And we’re having those conversations at the same time.”

Time could be running shorter than many anticipated, after a new estimate from the Bipartisan Policy Center this week found that Treasury could run out of borrowing room under the debt ceiling some time in “early September.” Mnuchin said Wednesday after a meeting with GOP leaders that his agency was still evaluating and updating its own internal estimates, but corporate tax receipts have been coming in lower than expected.

Thune said he’s heard the date that Treasury might exhaust its borrowing authority could be around Sept. 10-12, which would leave very little time when lawmakers return from the August recess on Sept. 9.

“If in fact the trigger is reached by Sept. 10th or 12th, which is when they are predicting now that it could be, then yeah, I think we’re going to have to move. And then the question then becomes how, what’s the mechanism, what’s the process and is there something it can ride on,” Thune said.

Other estimates floating around are similar to the BPC’s figures. Wrightson ICAP, an independent research firm that analyzes Treasury financing trends, said Monday that while Treasury should have enough cash to make it until Oct. 2, balances “will be uncomfortably low in the first half of September.” If they can make it past Sept. 16, when quarterly tax revenue is due, it will “give Treasury added maneuvering room in the second half of the month.”

The differing approaches to spending caps, which are holding up a debt limit deal, are pretty stark.

The House has passed 10 of the 12 appropriations bills for next year so far, adhering to overall limits of $733 billion in defense funds and $647 billion for domestic and foreign aid programs, not counting adjustments for disaster relief programs.

The White House’s fallback plan would codify, at least for one year, the comparable fiscal 2019 numbers: $716 billion for defense and $605 billion. For the administration, that’s a compromise from their preferred levels of $750 billion for defense and nearly $544 billion.

At one point Senate Appropriations Chairman Richard C. Shelby, R-Ala., had floated the possibility of marking up fiscal 2020 bills to the same current-year levels, but Senate Majority Leader Mitch McConnell, R-Ky., has put the kibosh on that plan pending a global deal with the Trump administration and House Democrats.

Thune said he didn’t have a good answer for how to resolve the disputes over spending caps and be able to raise the debt limit on time. He took the unusual step of casting a wider net for solutions. “Good question,” he told reporters. “Do you have a suggestion about that?”

Paul M. Krawzak contributed to this report.