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The "Boehner Rule" died today.

Speaker John Boehner once coined that phrase based on this conservative principle: Any increase in the nation's debt ceiling would be accompanied by an equal dose of spending cuts.

The rule has sparked a series of fiscal fights that have often left Capitol Hill frozen in gridlock. But it was set aside today as Boehner prepared to call a vote tonight on raising the nation's borrowing power - with no strings attached. It's a rare moment for Boehner, who is bringing legislation to the floor that is not supported by a majority of Republicans and will must rely on Democratic votes to pass.

"You all know that our members are not crazy about voting to increase the debt ceiling," Boehner said today, venting frustration that President Obama has refused to negotiate on the debt ceiling. "So the fact is we'll let the Democrats put the votes up. We'll put a minimum number of votes up to get it passed."

For Boehner, it's a significant change in course. He floated a plan tying the debt limit increase to a bill that would have reinstated cuts to benefits for military veterans, but that idea was rejected by conservative Republicans and a fear that Democrats would not follow suit, which would have left Boehner with another fiscal fight on his hand.

"We've lost the stomach for brinksmanship," one Republican lawmaker told ABC News, speaking on condition of anonymity to describe the mood and mindset inside the closed-door Republican meeting today where Boehner announced his plan.

When asked today by reporters whether the "Boehner Rule" was dead, the speaker simply declared: "I would hope not. As I've said before, this is a lost opportunity."

While the decision by Boehner is an embarrassment on one level, yet another sign that he is unable to guide his rebellious Republican conference, it also is something of a relief. Republicans are eager to keep their election-year focus on criticizing the nation's health care law, without giving Democrats fresh ammunition to accuse them of being obstructionists.

Boehner said he "would expect virtually every Democrat to vote for it," but it remained an open question how many actually would. That was the key question, with Boehner being forced to round up the remaining votes from Republicans, to make sure the legislation actually passes.

"We're going to have to find them," Boehner said. "I'll be one of them."

Vice President Joe Biden, visiting the Capitol today, did not suggest it would be a challenge finding Democratic support. He said he was pleased Republicans were moving forward.

"Look, if a clean bill comes up and it passes, that's all I care about," Biden told ABC News, "no matter what the makeup of the votes are."