Demonstrators hold placards during a Planned Parenthood rally outside the State Capitol in Austin on Wednesday. (Ilana Panich-Linsman/Reuters)

Antiabortion groups thought they had a sure way to slash funding for the country’s largest abortion provider as part of the health-care overhaul proposed by the House Republican leadership.

But the overhaul failed — a nascent effort to revive it has also stalled — dampening conservatives’ once-high hopes to achieve one of their dearest goals: defunding Planned Parenthood.

Abortion opponents are not giving up the fight. They say there still is a chance to pass a budget measure including major cuts to Medicaid funding for the women’s health group — without any Democratic support.

The first attempt to defund Planned Parenthood using special budget procedures was through the 2017 budget measure that also carried the House GOP health-care plan. It’s on pause as House Republicans remain badly divided about their next move on health care.

Yet abortion foes are holding out hope that the effort will be resurrected after Congress returns from a two-week recess. They don’t have a contingency plan in place if Congress fails to reach a deal on rolling back and replacing the 2010 Affordable Care Act.

“We really haven’t developed a Plan B,” said Tony Perkins, president of the Family Research Council, a group that has pushed for defunding Planned Parenthood as part of the effort to repeal and replace the Affordable Care Act.

Conservatives say they have not moved to conversations about alternative ways to defund Planned Parenthood — although they are not planning to pick a fight in the spending discussion this month. Congress must pass a bill to keep funding the government past April 28. For now, they are keeping their eyes on the Obamacare repeal efforts as their best chance of success.

“I think reconciliation remains by far the ideal way,” said Rep. Trent Franks (R-Ariz.), chairman of the House Pro-Life Caucus, referring to a procedural maneuver that allows the Senate to pass something with a majority vote.

“Really, everyone’s head is down in this moment,” said Marjorie Dannenfelser, president of the antiabortion group Susan B. Anthony List.

Top conservatives including Dannenfelser attended a meeting at the White House on Tuesday with Vice President Pence, who has been trying this week to forge an agreement on an Obamacare repeal. But their hopes dimmed again Wednesday morning, as key members indicated that little progress has been made on bringing conservatives and moderates closer together.

The state of play is a shock to Dannenfelser and others, who never expected things to turn out this way. They thought they had perfectly laid the groundwork for success by getting Planned Parenthood defunding included in a test vote last year to repeal the health-care law and by extracting a promise from then-presidential candidate Donald Trump during his campaign that he’d sign it.

“This is like some nightmare we couldn’t have conceived on our own,” Dannenfelser said.

What makes the situation even more bitter for antiabortion activists is that there’s little dispute among House Republicans about blocking Planned Parenthood clinics from getting Medicaid dollars, which represent about 30 percent of the health provider’s budget.

A few Senate moderates — including Sens. Susan Collins (Maine) and Lisa Murkowski (Alaska) — oppose defunding Planned Parenthood. But beyond those senators, the issue represents one strong point of GOP agreement on the health-care bill.

“The good news is that pro-life issues . . . [were] the base of the bill and a nonnegotiable issue,” said Tom McClusky, a lobbyist for March for Life.

The House voted in September 2015 to freeze Planned Parenthood’s funding for one year, after undercover videos purportedly showed officials talking about the selling of fetal tissue. Senate Democrats blocked that effort, but with Trump in the White House, abortion opponents seized an opportunity to defund Planned Parenthood through the budget.

“You couldn’t possibly go wrong. [It is] the top priority of the president, the must-pass piece of legislation,” Dannenfelser said. “We know we have the votes. The skids are greased, ready to go.”

The American Health Care Act, the bill from House Speaker Paul D. Ryan (R-Wis.) to replace Obamacare, would essentially block Planned Parenthood clinics from getting Medicaid payments for one year. Medicaid and other taxpayer dollars can’t be used for abortions, but conservatives argue that the money is all fungible and should not go to any providers of abortion services.

Planned Parenthood has been defending itself in part by playing up the non-abortion health care services it provides — such as contraception and cancer screenings — and even running ads featuring a patient talking about how a Planned Parenthood doctor encouraged her to give birth to her son instead of having an abortion.

“One in five women has gone to Planned Parenthood for care in her lifetime,” Planned Parenthood President Cecile Richards said. “Every single member of Congress represents a Planned Parenthood patient, former patient or supporter. You cannot attack Planned Parenthood without serious consequences.”

Planned Parenthood remains the country’s largest abortion provider, however, and will remain a key target for opponents who had hoped to see the end of their long-standing battle with the help of one-party GOP rule in Washington.

Franks said if the stalled health-care discussions ultimately result in a better bill, it was “worth the challenge.”

“If we lose, it’s a tragedy,” he said.

If Congress and the White House ultimately don’t follow through, conservatives are threatening retribution.

“If it isn’t done at all, there will be a lot of new faces in January 2019,” McClusky said.