As advocacy groups withdraw support for a Senate-passed bill to protect lesbian, gay, bisexual and transgendered employees from discrimination in the workplace, Minority Leader Nancy Pelosi signaled on Thursday that she was still prepared to support the legislation should it come to the House floor.  

“I think it would be a great advancement,” the California Democrat said at her weekly news conference. “Everybody has to make an accommodation.”  

A coalition of influential LGBT rights organizations jointly pulled endorsements earlier this week of the legislation, partly in protest of the recent Supreme Court Hobby Lobby decision. The Senate bill’s “conscience clause,” they said, is now too bitter a pill to swallow.

The American Civil Liberties Union, the Gay & Lesbian Advocates and Defenders, Lambda Legal, the National Center for Lesbian Rights and the Transgender Law Center wrote:

“The provision in the current version of the Employment Non-Discrimination Act (ENDA) that allows religious organizations to discriminate based on sexual orientation and gender identity has long been a source of significant concern to us. Given the types of workplace discrimination we see increasingly against LGBT people, together with the calls for greater permission to discriminate on religious grounds that followed immediately upon the Supreme Court’s decision last week in Burwell v. Hobby Lobby, it has become clear that the inclusion of this provision is no longer tenable. It would prevent ENDA from providing protections that LGBT people desperately need and would make very bad law with potential further negative effects.”

There are currently no plans to move the legislation in the House, where Speaker John A. Boehner, R-Ohio, has repeatedly signaled he was not supportive. “The Speaker believes this legislation will increase frivolous litigation and cost American jobs, especially small business jobs,” said Michael Steel, Boehner’s spokesman, late last year.  

The religious exemption provided in the Senate bill was originally included in exchange for workplace protections for transgendered individuals.  

The Senate measure’s protections for the transgendered  made the bill a difficult choice for many Senate and House Republicans, even those who had supported ENDA in the past.  

But if GOP leadership does agree to move ENDA through the legislative pipeline, Pelosi said she would still be inclined to vote for it, determined not to let the perfect be the enemy of the good.  

“I think so,” she said when asked directly what position she would take.