By passing the bill, Republicans hope to eliminate a fund that they have called a "slush fund," and even direct $1 billion of that fund for deficit reduction.

But the bill could be up for a tough vote — some conservatives say the GOP shouldn't be helping any piece of ObamaCare survive, and most Democrats are expected to vote against the bill.

The House is expected to approve the rule for the bill in the early afternoon, after which it will hold general debate and consider two amendments.

Also in the House, members will consider a bill to honor the four girls killed in a 1963 bomb attack in Birmingham, Ala.

And, members will consider a bill making a technical change to a law dictating how the U.S. Mint can make Baseball Hall of Fame commemorative coins.

The Senate starts at 9:30 a.m., and sometime in the afternoon, senators are expected to vote on a motion to proceed to S. 743, the Marketplace Fairness Act. This bill would allow states to collect sales taxes from online companies, on sales made to residents of states that have a sales tax.

Votes on amendments to this bill are also possible as early as today.

At noon, the Senate will hold two nomination votes, one of which is on Sylvia BurwellSylvia Mary Mathews BurwellPrice was a disaster for HHS — Time for an administrator, not an ideologue Overnight Healthcare: GOP chairman to introduce pre-existing condition bill ObamaCare enrollment hits 11.5M for 2017 MORE to be the Director of the Office of Management and Budget.

The other vote will be on Jane Kelly to be a U.S. Circuit Judge for the Eighth Circuit.