(CNN) — A key House GOP negotiator warned on Friday that efforts to lock down a debt limit deal could either quickly come together or fall apart entirely – a warning sign as lawmakers and the White House race the clock to try to secure an agreement to prevent a first-ever default.

“There is forward progress,” Rep. Patrick McHenry, a chief GOP negotiator, told CNN after he left the speaker’s office. “But each time there’s forward progress, the issues that remain become more difficult and more challenging. So that is step-by-step, small-step-by-small step, and at some point, this thing can … come together or go the other way.”

But in a major development Friday afternoon that will give lawmakers more time to reach and pass a deal, Treasury Secretary Janet Yellen said that Congress must address the debt ceiling by June 5 or the US Treasury will not have enough funds to pay all of the nation’s obligations in full and on time. Previously, Yellen had estimated that the earliest possible day default could occur was June 1.

There have been signs that negotiations over raising the nation’s debt limit have gained some momentum, but major differences between the two sides still remain and time is running short as the risk of default grows.

One of the most critical issues in the talks has been spending cuts, which Republicans have demanded in exchange for voting to raise the debt limit. But there were also a series of outstanding issues beyond spending levels as of Thursday night, with the two sides especially far apart on work requirements for social safety net programs.

“Hell no,” Rep. Garret Graves, another key GOP negotiator, told CNN when asked if Republicans were willing to drop work requirements on social safety net programs to get a deal on debt ceiling.

“Hell no, not a chance,” he said and suggested the issue centers on work rules for food stamps and temporary assistance programs for needy families, not Medicaid.

“Everything’s complicated,” McHenry said. “Everybody wants the details but the larger issue here is an agreement that changes the trajectory of our nation’s finances. And that’s what we’re working on. And that makes it difficult. It’s of consequence.”

Asked if a deal could come together Friday, House Speaker Kevin McCarthy emphasized they are working as hard as they can.

“We know it’s a crunch time,” McCarthy said. “So we’re going to work just as hard, we worked through the night last night. I thought we made progress yesterday. I want to make progress again today and I want to be able to solve this problem.”

Under a potential agreement being eyed by negotiators, the debt ceiling would be raised for two years while also capping federal spending – except for defense and veterans spending – for the same period, two sources familiar with the negotiations said. A separate source familiar with the negotiations said that the two sides were still working out details on the length of the spending caps deal, which Democrats have insisted should only last for as long as a debt ceiling raise.

If and when a deal is secured, legislative text will still need to be written and congressional leaders will have to lock down votes and shepherd a bill to passage through both chambers. None of that will be easy or instantaneous and any number of pitfalls could emerge along the way.

The stakes are only growing steadily higher as the US moves closer to a potential default with each passing day.

With no bill to vote on, House lawmakers left Washington for the Memorial Day weekend and will be given 24 hours’ notice to return if and when a deal is reached.

Adding to uncertainty is the fact that debt limit deadline predictions aren’t clear cut. Rather than a set-in-stone deadline, they are more of a best guess estimate, which makes it far harder to know exactly how much time Congress has to act to avert potential financial catastrophe – and increases the odds that lawmakers could inadvertently trigger a default by not acting soon enough.

The Treasury Department has stressed this uncertainty in urging Congress to act. “It is impossible to predict with certainty the exact date when Treasury will be unable to pay all the government’s bills,” Yellen wrote in her letter to McCarthy on Monday.

“We have learned from past debt limit impasses that waiting until the last minute to suspend or increase the debt limit can cause serious harm to business and consumer confidence, raise short-term borrowing costs for taxpayers, and negatively impact the credit rating of the United States,” Yellen warned.