Reproductive rights advocates on Wednesday branded a 20-week abortion ban, due for a House vote on Thursday, as an attack on women’s health and a candidate for a Senate filibuster amid signs that some GOP support for the measure may be weakening.

Democratic lawmakers, along with NARAL Pro-Choice America and other abortion rights groups, gathered on Capitol Hill to protest the bill (HR 36), which will be considered the same day as an annual anti-abortion rally in Washington, D.C. The measure would bar abortions after 20 weeks of pregnancy, except in the cases of rape, incest or when the mother’s life is in danger.

“This bill is going nowhere, and it’s going nowhere fast,” said Sen. Barbara Boxer, D-Calif., predicting the measure wouldn’t have enough support to overcome a filibuster. “Even if it does, the president would veto it.”