Amid partisan brawls over abortion and contraception, some Democrats saw the Violence Against Women Act as the next battle in what they framed as a Republican “war on women.” But Senate Republicans did not rise to the bait. Republican senators like John Cornyn of Texas made clear their concerns, but even before amendments to address those concerns were voted on, many of the same senators who had expressed reservations signaled that they would vote for the bill, regardless of whether it was changed. No Republicans spoke out against it before the final tally.

“I intend to vote for the underlying bill even with its flaws,” Senator Kay Bailey Hutchison of Texas announced even as she pressed for changes, including one that would limit advertising on Backpage.com, a Web site that has an “adult services” section.

If there are to be fireworks, they will have to come when the Senate version comes up against the House’s. House Republican women this week announced that they would introduce a version of the violence act when they return from next week’s recess, with a final House vote expected by mid-May.

The House bill is likely to be stripped of three provisions that have incensed some conservatives. One would subject non-Indian suspects of domestic violence to prosecution before tribal courts for crimes allegedly committed on reservations. Another would expand the number of temporary visas for illegal immigrant victims of domestic violence. The last would expand Violence Against Women Act protections to gay, bisexual or transgender victims of domestic abuse.

“We’re not going to be looking at the controversial issues,” said Representative Sandy Adams of Florida, who is the main sponsor of the impending House bill.