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.”

Democratic Sen. Patty Murray of Washington added that “if Majority Leader [Mitch] McConnell chooses to take up this bill, which is nothing but a direct attack on Roe v. Wade  . . .  we’ll know what his real priorities are.”

Members of NARAL Pro-Choice America, amid a backdrop of pro-abortion protesters carrying signs, said they would be delivering a petition with more than 100,000 signatures to McConnell asking him to not consider the bill on the Senate floor.

Meanwhile, Republican Reps. Renee Ellmers of North Carolina and Jackie Walorski of Indiana have withdrawn their co-sponsorship of the measure, although Walorski wrote in a Facebook post that she still intends to vote for the bill — as she did in 2013.

The House Rules Committee may meet late Wednesday to draft a new rule for debate that removes or changes legislative language.

The House Pro-Choice Caucus, led by Democrats Louise M. Slaughter of New York and Dianna DeGette of Colorado, said in a press release that “women in the GOP conference are rebelling against GOP leadership over the offensive language.” The lawmakers pointed to a provision in the bill that only allows exceptions for rape and incest if the incidents are reported to authorities.

The bill teed up by the House Rules Committee is identical to the one passed by the chamber in the 113th session that carved out the exceptions, with no amendments made in order.

“There’s been some confusion, but it is in fact the same one passed in June 2013,” said Douglas Johnson, legislative director of the National Right to Life Committee. “Some of the members mentioned in the press as raising questions about the clause have also reaffirmed in recent days they intend to vote for HR 36 as written.”

The rally coincided with Democratic lawmakers reintroducing legislation to limit the restrictions affecting abortions and other reproductive services. Supporters said the bill would prevent states from imposing “burdensome” and “unnecessary” requirements that target providers and cause abortion clinics to shut down.

“We’ve seen continuous and constant attacks  . . .  designed to sound like they safeguard women’s health when they are really sabotaging it,” said bill sponsor Sen. Richard Blumenthal, D-Conn. “The threat to women’s health care and reproductive rights is urgent, clear and present.”

Lawmakers said while many of the restrictions are taking place at the state and local levels, they remain concerned about the pace of measures being introduced in Congress that they believe would diminish reproductive rights.

Some states have seen a “record number of laws to curtail a woman’s right to choose,” said Sen. Tammy Baldwin of Wisconsin, who co-sponsored the measure along with 31 other Democrats. “Women are more than capable of making their own medical decisions without consulting the local legislators.”

Anti-abortion groups fired back in a press call Thursday, arguing that the Democratic measure would invalidate abortion restrictions that are permissible under the Supreme Court’s landmark decision in Roe v. Wade. “This is a very radical piece of legislation,” said Johnson of the National Right to Life Committee. However, “we think it would be a fine thing for every senator to go on record” about the bill, along with the House’s abortion ban measure.

While the 20-week ban is expected to pass on a largely party-line vote, the White House has threatened to veto it, arguing that the bill violates a woman’s right to choose. The administration also took issue with the rape and incest reporting language tucked into the measure.

The bill “demonstrates a complete disregard for the women who experience sexual assault and the barriers they may face in reporting,” the release said. “Research indicates that the majority of survivors have not reported their sexual assaults to law enforcement.”