The expectation that a debt deal may be forthcoming from talks between Senate Majority Leader Harry Reid and Republican leader Mitch McConnell is "very possible," Sen. Bob Corker, R-Tenn., told CNBC on Monday.
"I've had some good conversations early this morning. It is between Mitch and Harry. And I think people want to see that come to fruition," said Corker, a member of the Senate Banking Committee.
But, he added in a "Squawk Box" interview, "the wildcard is what happens if we do something here when it goes over the House."
It's widely acknowledged that agreements between Republicans and Democrats need to be reached on two fronts. They have to raise the nation's borrowing limit before the Thursday deadline set by the Treasury, and end the government shutdown now in its 14th day.
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Corker said both sides in the Senate are now in a place, grounded in reality. "Let's face it. Republicans have overreached on the health-care bill," he said of the strategy of linking a delay in funding for Obamacare to an agreement on the debt ceiling. He said Democrats had been trying to "actually bust or break the budget control act, which is also settled law."
But he stressed there's a "major expectations game to manage" in the House.
"We're not going to solve the biggest [debt] issues over the next three days," Corker said. "If we can do something for a period of time to get us to that place, maybe we finally do those things that we all know need to happen and have been working on for so long."
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That point may come in mid-January. "We keep putting off these episodes. But on the other hand, the moment—the sort of 'twitching hour'—is when this next level of sequester kicks in on Jan. 15. That's a pressure point that Democrats don't want to see happen."
Corker concluded, "Maybe it's that point in time when we have the opportunity ... to substitute some longer-term mandatory spending reforms" in place of the across-the-board sequester spending cuts.
—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.