As advocacy groups withdraw support for a Senate-passed bill to protect lesbian, gay, bisexual and transgender employees from discrimination in the workplace, Minority Leader Nancy Pelosi signaled 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.