The Senate is closing in on a bipartisan deal to reopen the shuttered government and raise the nation's debt ceiling by an Oct. 17 deadline.

Sen. Bob Corker said Republicans and Democrats could have an agreement by Tuesday afternoon. He said some of the details needed to be finalized, but the basic outline of a deal is set.

It would fund the federal government at $986 billion until Jan. 15 and raise the debt ceiling until Feb. 15. The deal would make changes to the new health care law, potentially eliminating the medical device tax and requiring income verification for those receiving health care subsidies.

The proposal would require the two parties to come up with a comprehensive and long-term budget deal by Dec. 15.

Senate Majority Leader Harry Reid, D-Nev., on the Senate floor cited "tremendous progress," and a smiling Senate Minority Leader Mitch McConnell, R-Ky., called it "substantial progress," adding, "We look forward to making more progress in the near future."

Senators met behind closed doors much of Monday and cancelled a meeting at the White House with President Obama to speed along the productive talks.

"There's a pretty good understanding of what one might look like," Corker said of the deal under discussion. "The thing isn't really final. "