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 CruzRafael (Ted) Edward CruzSenate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea GOP state lawmakers meet to plan possible constitutional convention MORE (Texas) and Mike LeeMichael (Mike) Shumway LeeOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea 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 ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (D-Nev.) and Mitch McConnellAddison (Mitch) Mitchell McConnellSenate passes 0B defense bill Overnight Health Care: New GOP ObamaCare repeal bill gains momentum Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea 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.