By Erik Wasson and Kevin Bogardus - 07/30/13 04:23 PM EDT
Sen. John McCainJohn McCainFULL SPEECH: Tim Kaine accepts Democratic VP nomination Retired admiral: It would be a disaster if Trump were the face of the U.S. Panetta's Trump attack thrown off course MORE (R-Ariz.) on Tuesday said secret White House debt talks remain "circular" days before the five-week August recess.
“We talk a lot, and we’ve come up with some principles and some numbers. It’s very tough,” McCain said. “The only thing that is a little concerning is that we’re going out of session, and there’s not much going on in August.”
The White House lead in the talks is Denis McDonoughDenis McDonoughBenghazi Report and Hillary: What it means for Philadelphia White House bans Cabinet members from speaking at convention Overnight Defense: Benghazi report fallout | Nearly 50 dead after Istanbul attack MORE, President Obama's chief of staff. He has been having frequent talks with senators, which follows up on meetings Obama held earlier this year.
The government will shut down on Oct. 1 if Congress does not approve a new bill to fund the government. Later this fall, Congress will face a separate deadline to raise the nation's borrowing limit.
McCain said he has been having calls and meetings with senior White House staff “almost every day.”
“The way these things usually work, you talk and talk and talk, and then suddenly, and you reach an agreement,” he said.
Participants say they have tried to expand on elements in which the sides agree.
President Obama has floated cutting entitlement benefits by using a new inflation formula known as chained consumer price index. It would increase payments under Social Security and other programs at a lower rate to adjust for inflation. Obama has also proposed more means testing for Medicare.
McCain and other defense hawks are eager to turn off automatic spending cuts to the Pentagon. They have signaled some flexibility on tax issues. In 2014, the Pentagon is set to be hit with a $54 billion cut under sequestration.
Some Republicans have called for the party to only approve a government funding bill that defunds ObamaCare, a proposal McCain sees as foolish.
“It’s a nonstarter,” McCain said. “We are not going to defund ObamaCare until we have 60 seats in the Senate.”
Former Democratic Senate Budget Chairman Kent Conrad (D-N.D.) on Tuesday said he is optimistic the small group of GOP senate negotiators can strike a deal.
Conrad spent months trying to forge a grand bargain on deficit reduction with some of the members in the talks: Sens. Tom CoburnTom CoburnThe Trail 2016: Words matter Ex-Sen. Coburn: I won’t challenge Trump, I’ll vote for him Coburn: I haven't seen 'self-discipline' from Trump MORE (R-Okla.) and Mike JohannsMike JohannsTo buy a Swiss company, ChemChina must pass through Washington Republican senator vows to block nominees over ObamaCare co-ops Revisiting insurance regulatory reform in a post-crisis world MORE (R-Neb.).
“I think there is a chance, not to have a grand compromise, but to do something significant,” Conrad told The Hill.
He said both sides should shoot for another $2 trillion in total deficit reduction.
Reactions from other members of the talks were mixed. "I suppose we'll keep talking," said a glum-sounding Sen. Lindsey GrahamLindsey GrahamTrump: 'I hope' Russia is able to get Clinton's emails Syria activists cheer Kaine pick Vulnerable GOP senators praise Kaine MORE (R-S.C.). "I don't know when."
He said talks last week showed signs of progress and this week could be the point where things get going for real.
"I thought we had a really good week last week. I thought we become more focused in what we are looking at. The next meeting will be very, very important," he said.
"You can go two routes with this thing. You can try to deal with sequester only...I want to solve our fiscal problems," he said.
He said he wants as big a debt deal "as is achievable."
"The notion of substituting some mandatory spending reductions for some discretionary spending reductions is more sensible...the bigger thing might be a bridge too far," Corker added. "I think this week we'll have a better sense of which direction we're trying to go."
Corker declined to reveal the details of what either side has proposed so far.
"I think this is the most important thing we'll do this year if we can get it done," he said.
--This report was originally published at 12:23 p.m. and last updated at 1:41 p.m.