Fresh off their victory on a controversial health care overhaul, House Democrats are preparing to wade into a potentially divisive social debate over whether to ban employment discrimination based on sexual orientation and gender identity.

Democrats behind the push, led by House Financial Services Chairman Barney Frank (D-Mass.), one of three openly gay Members, are already surveying their ranks to determine support for the measure, with the aim of approving it by the end of May.

The House cleared a version of the legislation in 2007 with a wide margin padded by support from 35 Republicans. But that bill did not extend employment protections to transgender people, after proponents determined they couldn’t wrangle majority backing for that approach.

This time, Democratic leaders are committed to pursuing a discrimination ban that includes transgender people, lawmakers and staff said. And they believe that rapidly shifting politics surrounding gay rights, nudged along on the transgender issue by an aggressive lobbying campaign by advocates, will help them win the day. But the push faces resistance from a so-far-unknown number of Democrats, mostly from rural, socially conservative districts. Many of these lawmakers are eager to avoid what they consider a tough vote — pitting a sizable chunk of their constituency against base voters and wealthy donors — in an already challenging re-election environment.

The fact that the measure passed the House last Congress without the transgender provision “helps our Members understand that this is not toxic, because nobody that I know of lost any race because of it,” Frank said. “Secondly, we have done some education on the transgender issue, which we hadn’t done before.” Two years ago, he said, the matter was “too new.”

But one House Republican leadership aide said Democrats are proceeding with the ban, officially the Employment Non-Discrimination Act, at their own political peril. “The fact that the Democrat leadership are about to make 60-plus vulnerable Members vote for transgendered protections shows just how out of touch Speaker [Nancy] Pelosi [D-Calif.] is with the reality facing these Members,” this aide said, predicting the provision would prompt the majority to lose the support of Republicans who backed it in the last Congress.

The broader version of the bill, introduced in June by Frank, has gathered 199 co-sponsors, including six Republicans — support that the measure’s backers pointed to in making the case it is already close to clearing the 216-vote hurdle needed for passage. “We feel confident that we have the majority,” said Allison Herwitt, legislative director for the Human Rights Campaign, which has helped coordinate lobbying for a discrimination ban extended to include gender identity. “The Speaker is interested in looking at, after the health care vote and after the recess, is everybody in the same place?”

That effort started this week, as an informal whip team divided up names of rank-and-file Democrats to survey. It includes Frank and the two other openly gay Members, Rep. Tammy Baldwin (D-Wis.) and Rep. Jared Polis (D-Colo.). Rep. Joe Crowley (N.Y.), another member of that team — in addition to being a chief deputy whip and a vice chairman of the Democratic Congressional Campaign Committee — said he understands the vote will still cause heartburn in some corners of the Democratic Caucus. “I don’t know if it’s ever the right time to do some of the more difficult things,” he said. “I do think this is the right thing to do and it ought to be done.”

The measure must clear the House Education and Labor Committee before it hits the floor, and Chairman George Miller (D-Calif.) said he is still huddling with the business community and others to hammer out some remaining issues.

The U.S. Chamber of Commerce was officially neutral on the bill in the last Congress. Mike Eastman, the group’s executive director of labor policy, said the chamber remains that way, “but we’re clearly going to carefully monitor it as it goes through the process” to ensure no technical concerns arise.

Agriculture Chairman Collin Peterson (D-Minn.), a member of the Blue Dog Coalition who supported the bill in 2007, said he’s not sure about the transgender language and said he thinks there is still some discussion about exactly what will be in the bill. But Peterson said the issue in general is not as controversial as it is sometimes made out to be.

“I think it gets blown out of proportion,” Peterson said. “I don’t think it’s as controversial as some things are,” such as gay marriage.

One concern backers are working to head off as they measure support for the comprehensive approach: the threat of a narrowly drawn Republican alternative that simply strikes protections for transgender people. “We want to make sure we can withstand any potential recommit,” said Polis, referring to the Republican procedural maneuver that could complicate the Democratic endgame on the measure.

Consideration of the measure could set the stage for an even more politically dicey debate over whether gays should be allowed to serve openly in the military. Majority Leader Steny Hoyer (D-Md.) on Tuesday would not rule out consideration of legislation to repeal the military’s “don’t ask, don’t tell” policy. He noted that both Defense Secretary Robert Gates and Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, have said they support ending the policy and that the Pentagon is working on recommendations. HRC’s Herwitt has said her group will press to add the repeal to the defense authorization measure, but Hoyer said House leaders have no plans to do that.

Steven T. Dennis contributed to this story.