The vote on the Defense bill would occur under a suspension process.
The Senate voted 56-42 Tuesday to end debate on the nomination of Nina Pillard to serve on the D.C. Circuit Court.
Earlier Tuesday, the Senate also voted 56-38 to confirm Patricia Millett to the D.C. Circuit Court — the second most important court because it has jurisdiction over most federal agencies.
The Senate voted 57-41 to confirm Rep. Mel Watt (D-N.C.) as top housing regulator.
The House passed two bills on Tuesday to extend various authorities of the Department of Veterans Affairs, in votes that were held despite the absence of several dozen members.
Senate Minority Leader Mitch McConnell (R-Ky.) tried to challenge a Senate rule change that allows the majority to end debate on a nominee with a simple majority.
Sens. Carl Levin (D-Mich.) and Joe Manchin (D-W.Va.) voted with Republicans against the rule of the chair on Tuesday.
The House on Monday quickly debated and passed a bill that would make it easier for the federal government to prosecute people guilty of child abuse.
The House passed legislation aimed at discouraging frivolous patent lawsuits.
The House voted Wednesday to amend the Dodd-Frank financial reform law with the help of 36 Democrats, even though the White House has threatened to veto the bill.
The House on Wednesday advanced two bills that Republicans say would help create jobs.
The House on Tuesday approved suspension bills dealing with the Transportation Security Administration (TSA) and federal land use, finishing up work on the week's non-controversial bills.