Awe-struck by brutal new poll numbers and divided amongst themselves, Republicans are scrambling to bring the government shutdown and looming default crises to an end, but can’t quite figure out a way to walk back their lofty demands.

House and Senate Republicans are at odds over Speaker John Boehner’s (R-OH) proposed six-week debt limit hike. The House GOP, dominated by conservatives, supports the extension and wants to sustain the shutdown to keep fighting Obamacare. Senate Republicans, meanwhile, are feeling the pinch from the unpopular shutdown and want to re-open the government as part of any proposal to avert a default on the country’s debt.

“There are Republican senators who are interested in seeing a [government funding] provision incorporated in any debt limit proposal,” said one Senate Republican aide. “Whether that means they won’t support a proposal that only addresses the debt limit remains to be seen.”

Meanwhile, President Barack Obama is playing hardball. A Thursday meeting with House Republicans at the White House failed to yield an agreement as the president resisted their plan to extend the debt ceiling until Nov. 22 with the promise of budget negotiations before then.

“Staff talks last night, no decisions made, will pick back up today,” emailed a House Republican leadership aide.

Republicans were taken aback by an NBC/Wall Street Journal poll Thursday evening that showed their favorable ratings plummeting to an all-time low. More distressingly, the poll found a “boomerang effect” where the GOP’s shutdown goal of targeting Obamacare had backfired as the law’s approval rose despite a woeful rollout last week.

Democrats have their own divisions. Unlike Obama, whose only demand is a debt limit hike or continuing resolution be “clean,” congressional Democrats don’t want to pass one without the other.

“Cooler heads have prevailed, and Republicans have admitted a clean bill to avoid default should be the standard,” Senate Majority Leader Harry Reid (D-NV) said Friday. “However … they’re talking about extending the debt ceiling for two months or six weeks — please. We do not believe a six-week delay of a catastrophic default is enough time to give the economy the confidence it needs.”

The two parties are subtly moving closer to agreement. GOP leaders have all but abandoned their Obamacare demands and now simply want Obama to negotiate — over something, although it’s not clear what. The White House meetings, which took place Thursday with House Republicans and are scheduled to take place Friday afternoon with Senate Republicans, provide face-saving mechanisms to both the GOP (who can say Obama negotiated) and for Obama (who can say he didn’t concede anything).

But the government still has to be re-opened and the debt limit still has to be extended. What the end result will be remains unclear.