AUSTIN, Tex. — With little more than a week left in Texas’ 30-day special legislative session, a barrage of corporate advertising and activism has the potential to sink legislation restricting transgender bathroom use that has been a flash point in the state’s culture wars.

Social conservatives and the state’s powerful lieutenant governor, Dan Patrick, have backed the legislation. Gay rights groups, business groups and the House speaker, Joe Straus, one of the few powerful moderate voices in the Texas Legislature, have opposed it. But after the State Senate, where Mr. Patrick presides, passed a bill, a narrower one is showing few signs of life in the 150-member House.

The effort is now focused on the House version, but State Representative Jonathan Stickland, one of the bill’s 46 co-authors and a member of the Tea Party-backed Freedom Caucus, said he was pessimistic about its chances of being allowed to advance to a vote.

“I think the Straus team has already decided that they are not going to let it out,” said Mr. Stickland, who, like other members of the staunchly conservative caucus, persistently defies the speaker’s leadership. “This is clearly part of a national agenda that is being pushed by the progressive left, and I think that that is just all coming to a head here.”