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 Cruz (Texas) and Mike Lee (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 Reid (D-Nev.) and Mitch McConnell (R-Ky.) announced a bipartisan fiscal deal Wednesday after House Republicans failed to get enough votes to pass their own measure Tuesday.
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.