The Senate will vote first Wednesday on the bipartisan deal to raise the debt ceiling and end the government shutdown.

There had been speculation that the House might act first to speed passage of the legislation, but that was before Republican Sens. Ted CruzTed CruzGraham, Cruz proposal to defund the U.N. is misguided Right renews push for term limits as Trump takes power Dissenting nominees give hope to GOP skeptics of Trump MORE (Texas) and Mike LeeMike LeeRight renews push for term limits as Trump takes power Conservatives press Trump on Supreme Court pick Overnight Finance: Ethics chief blasts Trump business plan | Senate begins late-night marathon vote | Lawmakers look to rein in Trump on trade MORE (Utah) said they won't filibuster the bill.

A Senate Democratic leadership aide said the Senate would likely vote in the early evening Wednesday and then send the bill to the House, though exact timing is still being worked out.

Senate leaders Harry ReidHarry ReidDems want Sessions to recuse himself from Trump-Russia probe Ryan says Trump, GOP 'in complete sync' on ObamaCare Congress has a mandate to repeal ObamaCare MORE (D-Nev.) and Mitch McConnellMitch McConnellGOP senators introducing ObamaCare replacement Monday Senators introduce dueling miners bills Dems demand second hearing for Trump's Education nominee MORE (R-Ky.) announced a bipartisan fiscal deal Wednesday after House Republicans failed to get enough votes to pass their own measure Tuesday.

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The Senate bill would end the shutdown, fund the government through Jan. 15 and raise the debt ceiling until Feb. 7. It also calls for a budget conference between the House and Senate that would have to report back by Dec. 15, and requires stricter income verification for recipients of ObamaCare subsidies.

Rep. Devin Nunes (R-Calif.) told The Hill that the Senate is likely to vote on the bill around 5 p.m. and then the House would vote closer to 9 p.m. He also said the House would leave town after the vote and return on Tuesday.

Lawmakers are trying to get a bill to President Obama's desk before the U.S. Treasury reaches its borrowing limit on Thursday. 

The stock market was volatile throughout the more than two-week government shutdown and several financial institutions threatened to downgrade the U.S. credit rating if the U.S. defaulted on its debt.

- Molly Hooper contributed to this article.