The VAWA reauthorization bill, H.R. 4970, was introduced by Republicans in late April. The bill includes many elements of the Senate-passed bill, S. 1925, but unlike that measure, does not expand visas that illegal residents can use to win legal protections if they suffer domestic violence.
Republicans said the Senate's expansion of these visas adds to the deficit, and House passage of the GOP version could lead to further discussions on this issue in a House-Senate conference.
In a colloquy with House Minority Whip Steny Hoyer (D-Md.), Cantor did not answer questions about whether the VAWA bill would come up under an open rule that allows for various amendments to be considered.
Hoyer admitted that he and Cantor have had a better relationship over the last few weeks, and asked Cantor if he would consider allowing a vote on the Senate bill as a way to keep their relationship going.
"In light of the fact that you and I have been working in such a bipartisan fashion lately, perhaps that would be a good way to continue that process," he said. Hoyer later remarked that their colloquy was one of the "more tame" discussions they've had.
Cantor did not not answer as to whether a vote on the Senate bill would be possible, but agreed that their relationship, which was rocky last year in particular, has improved.
"There has been an improved sense of cooperation and I appreciate the gentleman's part in trying to deliver results and trying to make sure we get America back to work," Cantor said. He also indicated that their relationship is better in large part because they have found ways to focus on issues they can agree on, and said Republicans took a similar approach in the GOP's VAWA bill.
"The approach that we took … was to do what it is that the gentleman and I have been trying to in the last couple weeks, and that is to separate out things that divide us, and trying to unite us around a central focus," Cantor said.
Hoyer also pressed Cantor on which appropriations bill might come up next and whether all 12 would be done in the House before August, but Cantor said only that Republicans would continue with their open process. Just moments earlier, the House approved the first spending bill for 2013, funding the Departments of Commerce and Justice, NASA and other agencies.
Hoyer also warned Cantor about the deadline for concluding the House-Senate conference on a multiyear transportation bill, but Cantor said only that the conference is ongoing and that Republicans are aware of the end-of-June deadline for reaching an agreement.