File photo: U.S. Supreme Court Police guard the building during a protest against anti-abortion legislation at the U.S. Supreme Court in Washington, U.S., May 21, 2019.

WASHINGTON — Chief Justice John Roberts left open the possibility that he could side with the Supreme Court's liberal wing during intensive, fact-based arguments on Wednesday in a high-profile abortion case.

A vote with the court's four liberal justices to strike down a Louisiana law regulating abortion providers would be a dramatic turnaround for the chief justice, who joined a dissenting opinion from the court's decision striking down a similar law in Texas just four years ago.

Read more: Supreme Court abortion case tests Trump's campaign promise to overturn Roe v. Wade

But on Wednesday, Roberts suggested he saw that decision as binding. That ruling found that the Texas law had no medical benefits and placed an unconstitutional burden on women seeking abortion. Roberts twice said the medical benefits for the Louisiana law would likely be the same.

"I understand the idea that the impact might be different in different places, but as far as the benefits of the law, that's going to be the same in each state, isn't it?" Roberts asked of Louisiana Solicitor General Elizabeth Murrill at one point.

Wednesday's case was the first substantial abortion dispute to come before the top court since the confirmation of President Donald Trump's two appointees, Justices Neil Gorsuch and Brett Kavanaugh.

It marks a significant test of how the court's new conservative majority will treat laws concerning abortion. How the court ultimately comes down could have an impact on the next presidential election, in a race in which Trump has boasted of his impact on the federal judiciary and sought to develop conservative credentials on abortion.

The dispute concerned a Louisiana law that requires doctors who provide abortions to have admitting privileges at a hospital within 30 miles of their clinic, a requirement that could limit the state to just one provider. The court struck down the Texas law by a 5-3 vote in the 2016 case Whole Woman's Health v. Hellerstedt.

Roberts was in the dissent in the Whole Woman's Health case. But he raised questions a year ago by siding with the court's liberal members — Justices Ruth Bader Ginsburg, Stephen Breyer, Elena Kagan and Sonia Sotomayor — to halt the Louisiana law from going into effect while its challengers pursued their appeal.

There were not many clues presented during Wednesday's arguments as to how Trump's appointees will vote.

Gorsuch, who was largely expected to uphold the Louisiana law going into arguments, was unusually silent, asking no questions.

Kavanaugh, somewhat more of a mystery, quizzed Center for Reproductive Rights attorney Julie Rikelman about whether she believed that admitting privileges laws would be unconstitutional in every state, not just Louisiana and Texas. She said she believed they would be.

Justice Samuel Alito was the court's most talkative conservative on Wednesday, pushing Rikelman on whether her clients, an abortion clinic and several abortion doctors, should be allowed to bring the case in the first place.

Murrill and Justice Department attorney Jeffrey Wall, both in court defending the Louisiana law, argued that the clinic and doctors had a conflict of interest with the women whom they serve.

It was not clear whether the other conservative justices would sign onto Alito's point, but Breyer and some of the other liberals pushed back strongly.

Breyer, citing past abortion cases that had relied on so-called third-party standing, or the right of clinics to sue on behalf of their patients, said doing away with it would require overturning at least eight past Supreme Court rulings.

Breyer told Wall that if the court was going to reexamine third-party standing, "let's go back and reexamine Marbury v. Madison," the landmark 1803 ruling.

Sotomayor took issue with the idea that there were diverging interests between women seeking abortions and the clinics providing them.

"What sane woman who's a plaintiff is going to have a conflict with a doctor who wants to protect her rights by doing what they can to comply with the law?" she asked.

An overriding question during arguments — not least because it seemed to be on the mind of Roberts, the likely swing vote — was about the medical benefits that come from requiring abortion doctors in Louisiana to have admitting privileges within 30 miles of their clinic.

Read more: The battle over abortion rights: Here's what's at stake in 2020

Kagan said the clinic, known as Hope Medical Group, had performed about 70,000 procedures over 23 years and had only four hospital transfers.

"I don't know of a medical procedure where it's lower than that of any kind," she said.

Ginsburg pressed each of the attorneys specifically on the 30-mile limit included in the law, telling Murrill that it had "no necessary relationship" to where the women receiving the procedure actually live.

On the other hand, Murrill and Wall focused on the claimed burdens that the law would impose. They argued that in Louisiana, those burdens on abortion providers would be far more limited than in Texas.

A federal district court found that the burdens imposed by the law were unconstitutionally high, but that decision was reversed by the 5th U.S. Circuit Court of Appeals in 2018, which found that abortion doctors did not try hard enough to obtain admitting privileges.

Murrill leaned into the 5th Circuit opinion, claiming that it presented evidence that virtually all of the abortion providers "sabotaged their own applications."

The case is June Medical Services v. Russo, No. 18-1323.