(NBC NEWS) -- For this round of political brinksmanship, it's all over but the voting.
After Republicans agreed not to block a Senate bill to reopen the government and raise the debt ceiling, both houses of Congress were moving Wednesday to quickly pass the measure with bipartisan majorities.
The Senate is expected to vote first, with the House following suit Wednesday evening. Lawmakers released the final text of the bill shortly before the Senate vote was expected to begin.
Emerging from a closed-door meeting with his conference, House Speaker John Boehner formally announced that Republicans will not oppose the bill en masse, even as he warned that this budget fight surrender does not mean Republicans will stop attempts to change the president's health care law.
"The House has fought with everything it has to convince the president of the United States to engage in bipartisan negotiations aimed at addressing our country's debt and providing fairness for the American people under ObamaCare," Boehner said in a statement. "That fight will continue. But blocking the bipartisan agreement reached today by the members of the Senate will not be a tactic for us."
The leading Senate opponents of the Obama health law also said they wouldn't stand in the way of swift passage of the deal.
Sen. Ted Cruz, R-Texas, who led the initial charge in a marathon speech against Obamacare before the shutdown, told reporters that he wouldn't slow down the bill, although he would vote against it.
"There's nothing to be gained from delaying this vote one day or two days," Cruz said. "The outcome will be the same."
Sen. Mike Lee of Utah, a close ally of Cruz, said on the Senate floor that Republicans were right to fight the shutdown battle over opposition to Obamacare.
"Even if victory seemed difficult or impossible, that wouldn't excuse me or anyone else from doing the right thing," he said. "Avoiding difficult battles is, after all, how we ended up in this kind of mess."
The compromise bill will fund the federal government through Jan. 15 and extend the borrowing power, known as the debt ceiling, through Feb. 7. It also calls for an agreement by mid-December on a long-term budget plan.
Federal employees who were furloughed as a result of the shutdown will receive back pay "as soon as practicable," according to the bill's text.
While it raises the specter of further fights to come, the compromise at least puts an end a government shutdown that has dragged on for 16 days, leaving hundreds of thousands of workers without pay and doubtless hurting the delicate U.S. economy.
Ratings agency Standard and Poor's estimated Wednesday that the shutdown "shaved at least 0.6% off of annualized fourth-quarter 2013 GDP growth." That works out to a $24 billion bite out of the American economy.
The stock market, sensing an agreement, rallied Wednesday from the opening bell. The Dow Jones industrial average soared 205 points, and other indexes approached all-time highs.
Crucially, bond investors signaled they were less worried, too. Yields on short-term government debt, even loans coming due next week, fell sharply, a sign that investors felt surer that they would get their money back.
In the deal, Republicans failed to extract any major concessions on President Barack Obama's signature health care law, as they had hoped, other than tighter scrutiny on who gets federal subsidies for insurance.
Earlier, Boehner told WLW radio in Ohio that conservatives fought for their principles but that the time had come to pass a bill with a majority in the House.
"We fought the good fight," he said. "We just didn't win."
Republicans said that the 16-day ordeal offered lessons on how to approach future budget conflicts.
"I would hope that we learn from the past and employ different tactics and strategies that maybe would be more successful in the future," said Rep. Aaron Schock, R-Ill.
Rep. Charlie Dent,-R-Pa., said the effects of the shutdown on the party could be long-lasting.
"Is there short term damage, yes." He said. "Is there long term damage? We'll see."
The White House commended the Senate for its leadership, but Jay Carney, the press secretary, was quick to remind reporters of the economic damage already done.
"There are no winners here," he said. "The American people have paid a price for this. And nobody who's sent here to Washington by the American people can call themselves a winner if the American people have paid a price for what's happened."
By Carrie Dann, Political Reporter, NBC News