On Wednesday, Cantor said he would continue to work with Democrats on VAWA reauthorization. Both the House and Senate passed their own versions during the 112th Congress, but neither chamber took up the other's version. 

The Senate-version of VAWA extends protections for victims of domestic violence to Native Americans, LGBT victims and immigrants — this time without requiring more revenue and avoiding the "blue slip" problem. 

Democrats, including President Obama, said they preferred the Senate bill because it would give tribal authorities jurisdiction over non-Indians in domestic violence cases, but Republicans say that issue has raised questions about possible Constitutional violations.

Reid said he was hopeful that the Senate would pass the VAWA bill, S. 47, later Thursday.

“I’m optimistic the Senate will complete work today on the Violence Against Women Act,” Reid said. “But it means little if the House fails to act. … They failed to act last year and the women of America don’t want them to fail again this year.”

VAWA provides grants to victims of domestic violence in order to encourage victims to leave their abusive situations. Some feel they can’t get away from their abusers because they might not have another form of family income, so the grants can provide housing assistance and cellphones for victims. Under this reauthorization bill, these programs would continue for another five years.

The Senate also added the SAFER Act to S. 47, which helps law enforcement agencies address nearly 300,000 rape kit backlogs waiting to be analyzed across the country.