But Senate Majority Leader Harry Reid (D-NV) categorically ruled that out on Friday.
"Let's be absolutely clear: we are going to accept nothing that relates to Obamacare.," he told reporters after the bill passed, calling on Republicans to "get a life" and talk about something other than Obamacare.
That leaves House GOP leaders in a very tough spot. Their predicament is exacerbated by the fact that Sen. Ted Cruz (R-TX), the leader of the quixotic push to defund Obamacare, is privately telling conservative House members to defy Boehner's fiscal strategy, according to the National Review. Boehner has been trying to persuade members not to shut down the government over Obamacare by dangling all sorts of conservative goodies before them in a bill to lift the debt ceiling and stave off a catastrophic debt default.
"I very much hope that when the House bill comes back all 46 Republicans stand together, stand united against Obamacare," Cruz told reporters, standing beside Sens. Mike Lee (R-UT) and Marco Rubio (R-FL). "The House was always in a position where it was going to lead. And I know from my perspective and Sen. Lee's perspective we look forward to helping and supporting the House, standing up and doing the right thing for the American people."
Another possibility is a short-term stopgap bill of one or two weeks to buy some time. But as far as House GOP leaders are concerned, that's a long shot because it wouldn't resolve the differences and only lead to more tough votes.
House Republicans are scheduled to meet privately on Saturday to discuss these issues. Leadership aides declined to elaborate or discuss the possibilities they are considering.
"We're reviewing our options, and will discuss them with Members tomorrow," said Michael Steel, a spokesman for Boehner.
The lights go out on Monday at midnight in what would be the first government shutdown since 1996. Federal workers are on notice that they may be furloughed.