Senate Democrats are eager to push ahead with their bill to reauthorize VAWA, while Republicans are looking to advance their own version that does not increase the deficit and fixes elements that the GOP sees as problems under the current program.

That GOP bill may have been introduced Monday night, as a different VAWA bill was placed on the Senate calendar, S. 2338. However, Senate aides did not immediately confirm on Monday night that this was in fact the GOP alternative bill.

The Senate returns Tuesday at 10 a.m., and is expected to vote in the early afternoon on a GOP resolution disapproving of the National Labor Relations Board's union election rule. If that vote fails, the Senate will start holding votes on amendments to the postal reform bill.