WASHINGTON — House Democrats plan on Friday to push through broad legislation to uphold abortion rights, taking urgent action after a major Supreme Court setback as they brace for a ruling next year that could further roll back access to abortion nationwide.

The House vote will be largely symbolic given that the bill, the Women’s Health Protection Act, has little chance of advancing because of Republican opposition in the Senate. But House Democrats’ decision to consider it reflects their view that the issue could resonate strongly in the midterm elections next year, particularly if female voters see the Supreme Court action as a threat to rights that many believed had been long settled.

Democrats moved swiftly to schedule action on the measure after the court refused this month to block a Texas law that prohibits most abortions after six weeks of gestation. It would guarantee the right to abortion through federal law, pre-empting hundreds of state laws governing the procedure around the country. Democrats argue that it would codify Roe v. Wade, the 1973 Supreme Court decision that established a constitutional right to abortion.

The bill’s authors say they began drafting it a decade ago in response to emerging efforts at the state level to impose stringent requirements on those seeking and providing abortions, as well as the increasingly conservative makeup of the court. They say that the court’s current membership and its hostility toward abortion rights have validated the approach, and that time is of the essence because the justices are set to rule next year on a Mississippi law that severely restricts abortions.

“It became very evident that we needed to have something that would push back against all these state restrictions,” said Representative Judy Chu, Democrat of California and the lead author of the measure. “We could see that change was possible at the Supreme Court, and we knew we had to make sure that Roe v. Wade was protected.”

But opponents of the law — including some Republicans who have supported abortion rights — argue that it would go far beyond the landmark court precedent, stripping states of much of their ability to regulate abortion and impose measures intended to make the procedure safe. They say it would lead to many more abortions in the late stages of pregnancy.

“This legislation is really about a mandate by the federal government that would demand abortion on demand, without any consideration for anyone, including the conscience of the provider,” said Representative Cathy McMorris Rodgers, Republican of Washington and a chief foe of the bill.

Democratic backers of the measure say they are confident they have the support to win approval in the House, which has not previously voted on it. But the Democratic-led Senate might not take up the bill, which appears to be just short of majority support in that chamber.

At least two Democrats who oppose abortion rights, Senators Bob Casey of Pennsylvania and Joe Manchin III of West Virginia, are against the legislation. Senator Chuck Schumer of New York, the majority leader, has been reluctant to bring up measures in the evenly divided chamber that do not have at least 50 votes. Even if the bill could win a slim majority, Republicans would be certain to filibuster it, preventing it from advancing unless it could attract 60 votes, a number that seems far out of reach.

Senator Susan Collins of Maine, a Republican who backs abortion rights and was seen as a potential vote for the new bill, said she would not support it in its current form.

“I support codifying Roe,” Ms. Collins said. “Unfortunately, the bill that the House has drafted goes way beyond that.” She argued that it would “severely weaken” protections afforded to health care providers who refused to perform abortions on religious or moral grounds.

The Biden administration, pointing to the new Texas legislation, supports the bill.

“In the wake of Texas’ unprecedented attack, it has never been more important to codify this constitutional right and to strengthen health care access for all women, regardless of where they live,” White House officials said in a policy statement. “Our daughters and granddaughters deserve the same rights that their mothers and grandmothers fought for and won — and that a clear majority of the American people support.”

The Democrats’ strong push for the abortion rights measure reflects a changing political dynamic in the party. In the past, Democratic leaders were reluctant to emphasize measures such as the women’s health bill for fear of putting centrists in swing districts in a tough position and potentially alienating voters.

But as the ranks of centrist Democrats have shrunk, so have the numbers of lawmakers in the party who oppose abortion rights. Ms. Chu said she had found that her colleagues from competitive districts had been eager to sign onto the measure.

“This is a pro-choice nation,” Representative Jan Schakowsky, Democrat of Illinois and a chief backer of the legislation, told the House Rules Committee this week as she urged the panel to send the bill to the floor. “This is the majority view across most of the electorate.”

Multiple public opinion polls conducted since the Supreme Court agreed to take on the Mississippi case have reflected strong support for keeping abortion legal — nearly 60 percent in some surveys — though that support typically declines for abortions performed later in pregnancies.

Opponents say even those who may back abortion rights to some degree still want the procedure closely regulated and states to establish safeguards and limits.

“Our biggest issue is definitely that this takes away the ability of state lawmakers and local lawmakers to solve problems that they have identified and that their constituents raise,” said Katie Glenn, the government affairs counsel of Americans United for Life. “Thousands of state laws are at risk from this bill.”

Ms. Chu said it was some of those very laws that needed to be struck down, because their true intent was to make it more difficult to have abortions and to discourage women from seeking them. Although the measure was unlikely to clear the Senate, she said it was necessary that Democrats act given the Texas law and the probability of a major Supreme Court ruling after arguments set for December over Mississippi’s abortion restrictions.

“It is important for us to make a strong statement about what is possible in Congress,” Ms. Chu said, “to protect women’s freedom to make a choice.”