Sen. Rand Paul (R-Ky.), center, with Sens. John Cornyn (-Tex.), left, and John Thune (R-S.D.) speaks on Capitol Hill about Planned Parenthood. (Manuel Balce Ceneta/Associated Press)

Senate Democrats on Monday blocked a Republican-backed effort to end federal funding for Planned Parenthood following the release of undercover videos that raise questions about the practice of harvesting tissue from aborted fetuses for research.

The 53-46 procedural vote fell short of the 60 ayes needed to proceed with a bill that would immediately stop funding for the beleaguered women’s health-care provider. But the willingness of GOP leaders to bring the measure to a vote showed the new political importance of a social issue that had been sidelined just a month ago and heralded higher-stakes showdowns to come.

Defunding Planned Parenthood is now a centerpiece of the Republican agenda going into the summer congressional recess, and some hard-liners have said they are willing to force a government shutdown in October if federal support for the group is not curtailed.

“The time has come to have a full-throated debate about this, and the time has come to end all taxpayer funding for Planned Parenthood,” Sen. Rand Paul (R-Ky.), a presidential candidate and co-sponsor of the Senate bill, said Monday. “It’s about time we had a debate in our country about this, and it’s about time we said enough is enough.”

The undercover videos, produced by an antiabortion advocacy group known as the Center for Medical Progress, depict Planned Parenthood executives speaking, cavalierly at times, about the procurement of tissue from aborted fetuses. The producers had posed as biotech entrepreneurs in search of research specimens.

Antiabortion activists have suggested that the videos constitute evidence that Planned Parenthood has violated the federal ban on selling fetal tissue for profit, as well as other abortion restrictions. Although Planned Parenthood President Cecile Richards has apologized for the tone of remarks heard in one video, the organization has strongly denied any wrongdoing.

The videos have prompted investigations by two House committees and widespread calls from conservatives for a Justice Department investigation. Several Republican senators came to the Senate floor Monday afternoon to lambaste Planned Parenthood.

Sen. Joni Ernst (Iowa), a freshman tapped by GOP leaders to lead the defunding effort, accused the group of “harvesting baby body parts” and of engaging in “callous and morally reprehensible behavior.”

“It is wrong, the American people know it, and they should not be asked to foot part of the bill,” she said.

More than a third of Planned Parenthood’s $1.3 billion in revenue last year came from government sources.

Democrats have portrayed the move to defund Planned Parenthood as an assault on women’s health. Federal funding for abortion, they note, has been outlawed for decades; the bill under consideration in the Senate would block Medicaid reimbursements and federal family-planning grants that support cancer screenings, birth control counseling and other aspects of reproductive health. They also noted past Republican support for fetal tissue research.

Sen. Barbara Boxer (D-Calif.) said before the vote Monday that Republicans “have been out to get Planned Parenthood for decades. The only thing that changes are their tactics.”

Ending funding for the group, she added, would mean less access to birth control: “What they are doing will lead to more abortions.”

Republicans say community health centers and other providers would be able to accommodate the women served by Planned Parenthood’s roughly 700 affiliated clinics. Opponents of defunding say there is no way to easily serve the organization’s 2.7 million annual clients in other settings.

“If this bill went into effect, blocking our health centers from serving patients who rely on publicly funded programs for health care, millions of people would struggle to access quality reproductive health care — period,” said Dawn Laguens, executive vice president of the Planned Parenthood Action Fund.

Before the videos were released, GOP leaders had no plans to take up standalone legislation on Planned Parenthood this summer, and the issue was not widely expected to become a sticking point ahead of the Sept. 30 government-funding deadline. Instead, Republicans had expected to keep their political message focused on opposition to the Iran nuclear deal.

But the videos prompted outrage from the conservative grass roots — as well as from the four senators who are running for president. After fast-tracking the defunding bill to the Senate floor Wednesday, Majority Leader Mitch McConnell (R-Ky.) said the videos “literally shock the conscience.”

“It’s a simple choice,” he said. “Senators can either vote to protect women’s health or they can vote to protect subsidies for a political group mired in scandal.”

The GOP defunding push won the support of two Democrats on Monday: Joe Donnelly (Ind.) and Joe Manchin III (W.Va.). “Until these allegations have been answered and resolved, I do not believe that taxpayer money should be used to fund this organization,” Manchin said in a statement.

But those decisions did not change the arithmetic in the Senate, where 60 votes are necessary to consider legislation as deeply controversial as the Planned Parenthood measure.

Two other antiabortion Democrats, Robert P. Casey Jr. (Pa.) and Heidi Heitkamp (N.D.), did not support the bill, and Republican Mark Kirk (Ill.), who faces a difficult reelection campaign next year in a Democratic state, opposed proceeding as well.

McConnell also voted no Monday, a maneuver that allows him to restage the vote at a future date. But his greater challenge will be reconciling his own desire to demonstrate a “responsible, right-of-center governing majority,” as he put it in December, with growing conservative demands to stare down Democrats as the yearly funding deadline approaches.

The possibility of a shutdown received new attention last week after a group of 18 House Republicans told party leaders that they “cannot and will not support any funding resolution . . . that contains any funding for Planned Parenthood.”

Should Republicans propose defunding Planned Parenthood as part of any spending bill, “overwhelmingly, the Democrats would not support that,” House Minority Leader Nancy Pelosi (D-Calif.) said Thursday. The White House has separately threatened a veto.

McConnell and his leadership team have shied from addressing speculation that the issue might prompt a government shutdown, but other senators suggested using all leverage available.

Paul and Sen. Ted Cruz (R-Tex.), a fellow presidential candidate, have tried deploying some political jujitsu, suggesting that Democrats, not Republicans, would be responsible for any Planned Parenthood-prompted shutdown.

“I think that is an excellent question for you to ask every Democrat, if they are willing to try to shut down the government in order to force continued taxpayer funding from an organization that has now been caught on film apparently admitting to multiple felonies,” Cruz said Monday.

In a CNN interview Sunday, Paul said, “If President Obama wants to shut down government because he doesn’t get funds for Planned Parenthood, that would be President Obama’s determination to shut down government.”

Kelsey Snell and David Weigel contributed to this report.