The standoff over the debt ceiling and the government shutdown showed signs of softening Thursday.

House Speaker John Boehner said he would bring a temporary hike in the debt ceiling to the House floor in exchange for negotiations on government spending and taxes. Democrats say if the House votes to raise the debt ceiling and reopen the government, they will negotiate.

But how did we get to this point? Through a series of miscalculations and faulty assumptions on both sides.

A 'Hard Line'

The recent movement in the budget standoff seems to have been prompted by the fear of what happens if the United States can no longer borrow money to pay the bills it already owes.

President Obama accused the Republicans of purposely flirting with default, "thinking that it would give them more leverage."

"That's not my characterization. They've said it themselves. That was their strategy from the start," he said.

It certainly was part of Boehner's strategy. He always thought the debt ceiling was the better fight to have — because it theoretically gave him more leverage with the president.

In addition, says GOP pollster Bill McInturff, refusing to raise the debt ceiling was politically more popular than shutting down the government — mostly because few people know what the debt ceiling really is.

"The debt ceiling is a symbolic issue where people are allowed to express their frustration about too much spending in Washington," he explains. "And that is very comfortable terrain for Republicans and better positioning than a government shutdown. I understand that may not be, in fact, what the debt ceiling is about, but I'm describing in a symbolic way how the debt ceiling is perceived."

But it was the speaker who was forced to agree to raise the debt ceiling because he made an assumption that turned out to be wrong. He thought that Obama, under threat of default, would negotiate. After all, Obama had done this before — in 2011 — to his and the Democrats' disadvantage.

"The surprise to the speaker, I would suggest, has clearly been ... the president coming out with this hard line that he won't talk to him until the president gets what he wants first," says David Winston, a GOP pollster who works closely with the House Republican leadership.

Public 'Ambivalence'

Democrats also made assumptions that turned out to be wrong. They assumed the speaker had a plan for what he and his members needed to make a deal.

But Boehner has been whipsawed by his conservatives, and he's had to make it up as he goes along. On Thursday, he couldn't even say what he would need to end the crisis.

"I don't want to put anything on the table; I don't want to take anything off the table," he said. "That's why we want to have this conversation."

Democrats also miscalculated the politics of a government shutdown. They assumed the pain of a government closure, along with negative public opinion polls, would make Republicans budge. Although Republicans are now talking about a temporary hike in the debt ceiling, they're still not planning to reopen the government.

That's because so far there has been little public clamor, says political scientist John Sides.

"There's a lot of ambivalence in the public. There's maybe slightly more people that blame Republicans than blame Obama or Democrats, but the blame measure is much more equivocal than it was during the last major government shutdown under Bill Clinton in 1995 and 1996," he says.

'A Different Set Of Assumptions'

The mighty fortress of redistricting, which shields most Republicans from serious re-election challenges, also insulates them from outside pressure. Sides says there's also the surprisingly widespread belief among conservatives that a default wouldn't be so bad.

"There's a great deal of skepticism that not raising the debt ceiling will create any kind of serious economic consequences for the United States," Sides says. "So I do think that they're operating from a different set of assumptions about the way the world works and what price they might have to pay or not pay in this case politically."

When it comes to the debt ceiling, Republicans have already paid a political price — they've dropped delaying or defunding the Affordable Care Act as a demand. Now they seem focused on getting a deal around taxes and entitlements.

But Obama hasn't indicated yet what, if anything, he's willing to do to help the Republicans get down from the increasingly shaky limb they've climbed onto.

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