The House and Senate will vote tonight on a compromise proposal that would fund the government until Jan. 15 and extend the debt limit until Feb. 7.
The Senate plans to hold its vote late afternoon or early this evening, now that at least one key Republican, Sen. Ted Cruz, R-Texas, has said he will not stand in the way of a vote.
And the House vote will likely come late evening -- around 11 p.m. -- assuming the Senate has approved it.
The compromise was completed by Senate Majority Leader Harry Reid and Minority Leader Mitch McConnell after a House effort to offer a counter-proposal nearly derailed Senate negotiations.
The final agreement makes only insignificant changes to President Obama's health care law, by requiring income verification for people receiving health care subsidies from the government. And it also authorizes a bipartisan committee of negotiators to hammer out a long-term budget deal by Dec. 13, before government funding runs out again in January.
Senate Republican and Democratic leaders praised the compromise as a breakthrough.
"This compromise we reached will provide our economy with the stability it desperately needs," Reid, D-Nev., said on the Senate floor today.
"This has been a long challenging few weeks for Congress and for the country," McConnell, R-Ky., added. "It's my hope that today we can put some of the most urgent issues behind us."
And Republicans in the House, though they resisted it, rallied around House Speaker John Boehner today as he announced his willingness to move forward with the Senate bill.
One member leaving a House Republican Conference meeting this afternoon said Boehner received a standing ovation from the group. Another told ABC News that when the leadership asked whether any members objected to their plan to move forward with a vote on the Senate bill, none objected.
Boehner left without making comment, but shook his fist before cameras in a display of success.
In an interview this afternoon with ABC News, Tea Party Chairwoman Michele Bachmann, R-Minn., who has often clashed with the GOP leadership, said she was "very proud" of Boehner and she said he did "a wonderful job" holding the conference together.
"He was committed. We fought for the American people that was the issue," she said.
Boehner issued a statement pledging to continue working to dismantle Obama's health care law, but in an interview with an Ohio radio station, he was more blunt about the state of play.
"We did everything we could to get them to the table to negotiate, they just kept saying no. No, no, no," Boehner told ABC News Radio affiliate WLW-AM in Cincinnati. "So we fought the good fight. There's no reason for our members to vote no today."
A major obstacle that could have complicated plans to move the Senate proposal today appears to have been alleviated now that Cruz has said he would not block a vote.
"There's nothing to be gained from delaying this vote one day or two days," Cruz told reporters today as Senate leaders announced the agreement on the floor. "I never had any intention of delaying the timing of this vote."
Of the compromise, Cruz lamented that it does not provide "relief" to Americans from the Obama health care law.
"The United States Senate and the Washington establishment are doing nothing to provide relief to the American people," he added.
Neither the Senate plan nor a short-lived House GOP proposal defunded or postponed Obama's health care law, which was the center of tea party Republican demands for re-opening the government.
And even more modest concessions put forward by Boehner -- for example, to repeal the unpopular tax on medical devices and repeal government subsidies for congressional and administration staffers' health care -- could not get enough Republican support to pass.
Either way, however, Republicans now face the reality that they will not get any major concessions from Democrats in exchange for raising the debt limit and re-opening the government.
It will be an ignominious end to a saga that has ravished the party in public opinion polls and has raised doubt in financial markets that the two political parties are capable of resolving their differences.
ABC News' Arlette Saenz contributed to this report.