Wednesday: Setting up a final immigration vote in the Senate

The third is a motion to end debate on the underlying bill.

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Based on Monday's 67-27 vote in favor of ending debate on the Leahy language, all three votes are expected to succeed, which will allow the Senate to finally pass the bill late Thursday or sometime Friday. There was some discussion Tuesday about adding a group of non-controversial amendments to the bill, but it's unclear whether this will happen before the end of the week.

Senate Majority Leader Harry Reid (D-Nev.) said both parties are looking to add additional language, but said "I don't know if we can do it."

If the Senate agrees to end debate on the new language, the Senate would be able to vote as early as Thursday morning on final passage of the bill.

The House meets at 10 a.m. for speeches, and at noon it will consider a rule for three bills. Two of them are energy bills that will be passed later this week:

— H.R. 1613, the Outer Continental Shelf Transboundary Hydrocarbon Agreements Authorization Act, which implements an agreement with Mexico to allow for energy exploration on the U.S.-Mexico maritime border, and

— H.R. 2231, the Offshore Energy and Jobs Act, which would instruct the Obama administration to expand offshore lease sales to boost domestic energy development.

The rule also covers floor consideration of H.R. 2410, the Agriculture, Rural Development, Food and Drug Administration, and Related Agencies Appropriations Act. This last bill, however, won't be on the floor until July.

Members will also take up H.R. 1864, which would require the Defense Department Inspector General to investigate whether the reporting of rape or sexual assault has led to retaliation — currently, the IG must only look into sexual harassment.