They are considering moving a bill from a large group of House conservatives, known as the Republican Study Committee, that would require deep government spending cuts and other mandates in return for raising the debt ceiling through March 2017. It's not clear the plan can pass the House and, if it did, it would be a non-starter with Democrats in the Senate who have enough votes to block it.
But a "clean" debt ceiling bill, one that doesn't have spending cuts or other restrictions, can't pass the House either, Majority Leader Kevin McCarthy warned Tuesday.
"I do not see 218 for any clean bill," the California Republican said, referring to the number of votes needed for a bill to pass the House.
Asked about having enough votes to pass a clean debt increase in the House, Speaker John Boehner, who plans to leave Congress at the end of the month, said on Fox News, "that would be difficult," adding, "our members want real reforms."
But Boehner, whose departure has left an unresolved leadership struggle, ruled out a default and said there were "several different paths" that House Republicans were discussing later Tuesday at a meeting of all House Republicans.
Meanwhile, Senate leaders from both parties said they will wait for the Republican-controlled House to vote first before acting.
"We're going to wait to see how the House deals with that issue and respond accordingly," said Senate Majority Leader Mitch McConnell, who would not rule out passing a debt increase without conditions.
Bipartisan senators also signaled the negotiations over the debt limit would be separated from larger government funding talks with the White House, which would instead move on its own track. The shift is significant because the debt limit needs to be raised by November 3 in order to avoid a historic default on U.S. debt. It also shows that bipartisan fiscal talks between the White House and congressional leaders have so far yielded little progress.
"We have two issues: Debt ceiling, we have two weeks left on that. On the budget, we have until December 11. We're going to take them one at a time," said Senate Democratic Leader Harry Reid. "But until we get the debt ceiling done, I don't think there's going to be anything done of a serious nature."
With its procedural hurdles, the Senate would need several days -- close to a week -- to pass a bill raising the debt ceiling, one reason why senators are hoping the House will act quickly. Senate Democrats expect to provide the bulk of the votes on a clean debt bill with just enough Republicans joining them to be approved.
Sen. John Thune of South Dakota, the fourth-ranking Republican leader, acknowledged a clean bill would have trouble winning GOP support. But he added that the GOP was looking for a long-term debt ceiling increase until the spring of 2017 to avoid a divisive intraparty fight in an election year.
"It will be nice to do something through 2017 -- maybe spring of that year, so we are not dealing with this next year in an even hotter political climate," Thune said.
Thune, who chairs the Senate Commerce Committee, which has jurisdiction over much of the U.S. economy, insisted the country must not default on its obligations.
"The one thing that we realize is important is, as a nation, we've got to make sure that we're paying our bills," he said.