Labor Secretary Alexis Herman canceled a planned trip to California so she could continue to monitor the negotiations.
But there was a sense that momentum had been lost when, at midnight Sunday, Herman and all the parties left the hotel where federal mediators had guided 76 hours of talks over four days.
Hours after he urged them to "redouble their efforts" to reach a deal, Clinton, who was briefed on the status of the talks, predicted an agreement was near as he arrived Sunday night for a vacation on Martha's Vineyard, off the Massachusetts coast.
"It's my gut feeling they'll settle," the president told reporters. He held out his thumb and forefinger and said, "They're that close. It's a good deal. It will set a precedent for unions."
But Matt Witt, Teamsters communication director, said late Sunday that Clinton's optimism was unwarranted.
"It's unclear whether real progress will be made," Witt said before the sides broke for the night.
A Labor Department spokesman said the talks recessed about midnight and were set to resume at noon EDT today. Herman canceled plans to address the American Federation of Government Employees convention in Anaheim, Calif.
It was unclear whether in his comments Clinton was being optimistic or was trying to prod negotiators to end the nation's largest strike in more than two decades.
But there were signs earlier in the day that a deal was not a sure thing.
Teamsters President Ron Carey took a break from the talks for a teleconference to give union locals a status report.
He credited Teamsters pickets with forcing the company to begin serious bargaining, but added that many issues were under discussion and no agreements had been reached, according to union officials who heard the call.
Carey also urged them to continue plans for strike rallies in 30 cities on Thursday.
The walkout has revolved around the union's demand that more part-time workers be given full-time jobs and the company's desire to have its own pension plan with the Teamsters, replacing the current multiemployer one.
A company spokeswoman, Kristen Petrella, said "UPS' position is that since talks are ongoing, that's a good sign," but another company official said "no real progress" had been reported.
Yet leaders from both sides agreed Sunday that there had been more bargaining over the weekend than there had been in previous face-to-face sessions.
"There has been movement," Carey said on NBC's "Meet the Press." UPS Chairman James Kelly said on the same show, "The fact that we're continuing to talk is encouraging."
"We were at a make-or-break point last week, perhaps we are at another one right now," Kelly said on CNN's "Late Edition."
The strike by 185,000 workers has greatly inconvenienced small businesses that use UPS like their own shipping departments.
On a normal business day, the company delivers 12 million letters and packages. The strike is costing UPS up to $300 million weekly, and the Teamsters owe picketers $10 million in strike benefits.
The government said it lacked the legal authority to intervene and end the strike, and the Clinton administration was relying on Herman to keep the parties talking. Two earlier rounds of mediation ended inconclusively.