"The nerds have to work," McConnell spokesman Don Stewart said, referring to legislative staffers that are now writing the details.
The reported progress comes after House Republicans cancelled a Tuesday evening vote on a GOP proposal that failed to garner support from conservatives.
Without Democratic support, House Speaker John Boehner would have needed all but a handful of Republicans on board or else face an embarrassing defeat.
Earlier Tuesday, aides said the House would vote on a plan, but hope for passage waned after both Democrats and conservatives balked at backing it.
Heritage Action for America, a prominent conservative group, announced that it would "key vote" legislative action on the House proposal, holding "yes" votes against politically-vulnerable Republicans.
"Unfortunately, the proposed deal will do nothing to stop Obamacare's massive new entitlements from taking root — radically changing the nature of American health care," the group said in a statement.
(Read more: Reid: GOP proposal won't pass Senate)
The proposal would have funded the government until Dec. 15, raise the debt ceiling until Feb. 7. It would also strip lawmakers, their staff and members of the Obama administration of subsidies to buy insurance through the Affordable Care Act's exchanges.
White House Press Secretary Jay Carney comments on progress being made in the Senate on a budget deal that would reopen the government and avoid default, but adds that a resolution may be far away still.
Democrats were not on board with the GOP plan either. House Minority Leader Nancy Pelosi announced after a meeting at the White House that Boehner should be prepared to pass the bill "with 100 percent Republican votes."
GOP leaders pulled an earlier plan from consideration Monday morning after it became clear that it would not get enough votes for passage. But a spokesman for Boehner had pledged that a revised proposal would be put up for a vote by the end of the day.
The stakes are high for authorizing a new borrowing limit to avoid U.S. default on its debts before a Thursday deadline.
On Tuesday, Fitch Ratings put the U.S. government's AAA credit rating on "rating watch negative," citing uncertainty over the debt ceiling. And markets tumbled as lawmakers announced that separate Senate negotiations had been put on hold amid the House back-and-forth.