Senate Majority Leader Harry ReidHarry Mason ReidAmendments fuel resentments within Senate GOP Donald Trump is delivering on his promises and voters are noticing Danny Tarkanian wins Nevada GOP congressional primary MORE (D-Nev.) and Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenate passes 6B defense bill Poll: Kim Jong Un has higher approval among Republicans than Pelosi The Hill's Morning Report — Sponsored by PhRMA — Outcry raises pressure on GOP for immigration fix MORE (R-Ky.) adjourned the Senate for the week Thursday evening after having one more spat over how to proceed on legislation to reauthorize the Violence Against Women Act (VAWA).

Reid took the floor shortly after 7 p.m. to ask unanimous consent that the Senate take the House-passed VAWA bill, replace it with the Senate version, pass it and proceed to a conference with the House. He reiterated his view that the Senate bill does a better job protecting all women from domestic abuse.

"We don't believe that we should be in the business of picking and choosing which victims deserve protection," Reid said. "The House bill would roll back many important, long-standing protections in current law for abused immigrant victims, protections that have never been controversial."

Reid also rejected House complaints that the Senate bill adds a revenue measure, causing a "blue slip" problem with the House because under the Constitution, all revenue measures must originate in the House. Reid and other Democrats have accused Republicans of using this as an excuse not to move ahead to a conference.

But McConnell said Democrats are to blame for pushing on a bill that has this blue slip problem, and said Democrats are refusing a GOP proposal to move ahead.

"This is a problem that has been created by the majority, and I'm sorry they won't accept our offer to fix their problem so we can move forward," McConnell said. "It's not our fault that the Senate Democrats waited until well after VAWA expired to start moving a bill."

McConnell objected to Reid's request, and proposed his own solution — that the Senate bill be modified to take out controversial language on immigration that expands the availability of visas that illegal immigrants can obtain when they are victims of domestic abuse. The Democratic bill would expand access to these visas in a way that Republicans have said will increase the deficit by about $100 million.

But Reid objected to this proposal. "My first response is the amendment is something that conferees should be working on," Reid said. "We can't do that here without the proper input from all the interested parties."

Shortly after this exchange, the Senate adjourned until June 4, setting up the likelihood of more partisan fighting over how best to advance VAWA reauthorization legislation. Democrats in general have said their bill, S. 1925, offers better protections for Native American women, LGBT women and victims on college campuses or in subsidized housing.

Republicans, in contrast, have said their reauthorization bill, H.R. 4970, offers adequate protection to all and that Democrats are looking to expand the law in expensive and unnecessary ways.

Before adjourning, Reid passed dozens of non-controversial public health and military nominations, and passed a few bills by unanimous consent. One of these is S. 414, which is aimed at protecting girls in developing countries by preventing child marriage.

Another, S. 739, authorizes the Architect of the Capitol to add battery-charging stations throughout the Capitol. The Senate also approved H.R. 3992, a bill allowing Israeli nationals to get U.S. visas, along with a small number of other minor bills and resolutions.

The Senate will meet next for pro forma sessions on May 25, 29 and 31. It will reconvene on June 4, and on June 5 plans a procedural vote on S. 3220, which would amend the Fair Labor Standards Act to provide for more effective remedies for wage discrimination on the basis of gender.