Their plan to avert default fizzling, House Republicans are reportedly considering passing their bill and then skipping town.

According to Politico, House Speaker John Boehner (R-OH), House Majority Leader Eric Cantor (R-VA) and House Majority Whip Kevin McCarthy (R-CA) are discussing “voting on their bill and, if it passes, leaving town — a bid to try to force the Senate’s hand.”

House GOP leadership drew pushback Tuesday from both the White House and conservatives almost immediately after unveiling their debt limit proposal, which may not even have sufficient support to pass the lower chamber.

Boehner left open the possibility that the proposal may still be changed.

With the Senate closing in on a deal to avoid default and reopen the government, the House continues to represent a major obstacle.

Rep. John Fleming (R-LA) said Tuesday that House Republicans are trying to use the looming debt ceiling deadline to their advantage in negotiations with the Senate. Congress has until Thursday to increase the debt limit.

“We want to make a deal that they can’t refuse, and we’re running out of time,” Fleming said. “Timing is very important here. They’re going to be more motivated to take this up. Otherwise, they miss the Thursday deadline.”