While Reid, D-Nev., said there was not yet an accord, he said he hoped to have a proposal to outline when the two men and House leaders meet with Obama at mid-afternoon. Emerging from Reid's office, Sen. Amy Klobuchar, D-Minn., said "he told us the negotiations were productive and positive."
No details were available on the terms under discussion.
Visiting a Washington charity, Obama mentioned the possible progress in the Senate and said his mid-afternoon meeting will determine whether it's real.
"My hope is that a spirit of cooperation will move us forward over the next few hours," the president told reporters.
Otherwise, he warned that the threat of default was legitimate.
"If we don't start making some real progress both in the House and the Senate, and if Republicans aren't willing to set aside some of their partisan concerns in order to do what's right for the country, we stand a good chance of defaulting," he said.
In announcing the meeting with Obama, the White House said the president would repeat a vow he has made consistently in recent weeks: "we will not pay a ransom for Congress reopening the government and raising the debt limit."
The two Senate leaders, Reid and McConnell, had spoken by phone Sunday but failed to agree on a deal to raise the nation's borrowing authority above the $16.7 trillion debt limit or reopen the government. Congress is racing the clock with Treasury Secretary Jack Lew warning that the U.S. will quickly exhaust its ability to pay the bills on Thursday.
Separately, a bipartisan group led by Sen. Susan Collins, R-Maine, met for two hours Monday morning on a possible solution to the impasse.
"We're making very good progress, but there's still many details to be worked out," Collins said before joining her GOP colleagues at a meeting with McConnell. "We don't have a finished, agreed-upon product yet but I think we had an excellent meeting. And we'll get together later today."