Treasury Secretary Janet Yellen on Friday issued a new letter to Congress estimating that the government won't be at risk of running out of money to pay all its bills until June 5 -- slightly later than the agency's previous estimate of as soon as June 1.
"Based on the most recent available data, we now estimate that Treasury will have insufficient resources to satisfy the government's obligations if Congress has not raised or suspended the debt limit by June 5," Yellen wrote.
Republicans questioned Yellen's methodology, with some accusing her of "manipulation tactics."
"June 5? Yellen said it was June 1 earlier this WEEK. Republicans won't be intimidated by her manipulation tactics," tweeted Rep. Andy Biggs.
"Will the media join our efforts to demand Janet Yellen show her work? I have been asking for three months," said Rep. Bob Good.
As he headed to Camp David on Friday evening, President Joe Biden sounded optimistic about negotiations and hopeful that more progress will come into the night.
"There's a negotiation going on. I'm hopeful we'll know by tonight whether we are going to be able to have a deal," Biden said
"Things are looking good. I'm very optimistic. I hope we'll have some clear evidence tonight before the clock strikes 12 that we have a deal, but it's very close. And I'm optimistic," he added.
Rep. Patrick McHenry, a key GOP negotiator, agreed with Biden's comments that a deal is very close.
"I would concur," he said on his way into Speaker Kevin McCarthy's office Friday night.
"Everybody wants to look for the white smoke. We are not in that stage yet. So, you have to have an agreement, an agreement on the agreement, which is like the complicated part. You all know waiting around for you know the final bit of agreements is the hardest, longest wait and why we have all these gaps, and we have to go work through language," McHenry said.
McHenry said Biden's remarks "are a hopeful sign to me that I've rarely used that term in the last 12 days that I've been involved in this. So, hopeful sign that the President is saying those things, that tells me his White House team might be in a better disposition than what we've seen in previous days."
The update buys much-needed time for negotiators to hammer out a deal to raise the debt limit and avoid a disastrous default. The so-called "X-date" when the U.S. will run out of funds to be able to pay all its bills in full and on time has always been fluid, based on daily federal tax revenues and expenditures.
Lawmakers left Washington for Memorial Day recess with no deal in hand. McCarthy and Biden in recent days have said progress is being made but there is still no final compromise between both sides.
ABC News Senior Congressional Correspondent Rachel Scott has reported negotiators are eyeing a possible deal to raise the debt limit and increase defense and veteran spending for two years while also clawing back unspent COVID-19 funds.
But key hang-ups in the talks appear to be spending levels and work requirements.
Meanwhile, Yellen's letter comes as the Treasury Department's cash reserves are running dangerously low.
New Treasury data shows its cash balance dwindled to just $39 billion at the end of the day Thursday. This is down from roughly $60 billion at the end of last week – and $316 billion at the start of the month.
The Treasury also released data showing it holds roughly $67 billion in "extraordinary measures" it can use.
In her letter, Yellen noted that more than $130 billion of payments are scheduled in the first two days of June, including to Veterans and Social Security and Medicare recipients.
"These payments will leave Treasury with an extremely low level of resources," she wrote.
ABC News' Lauren Peller contributed to this report.