Clinics in Texas that were recently forced to stop providing abortions because of sweeping new regulations have filed an emergency appeal to the Supreme Court, arguing that the rules put an “undue burden” on women’s rights.

Only seven facilities can provide abortions to Texas’ women after an appeals court in New Orleans ruled last week that the state could enforce the full range of a sweeping anti-abortion law that passed in 2013. The remaining clinics are clustered in four cities; there are now none serving women west or south of San Antonio. According to the Center for Reproductive Rights, more than 900,000 women would have to travel 150 miles just to get to an open clinic.

The clinics are asking the Supreme Court to put the regulations on hold so that some can reopen while the legal battle plays out. If the court does not do so, the plaintiffs argue, “women’s ability to exercise their constitutional right to obtain an abortion will be lost, and their lives will be permanently and profoundly altered.” Clinics have already cancelled appointments and turned patients away. Once they lay off their staff, they “will likely never reopen.”

Whether the court will grant the emergency request or hear the full case remains to be seen. The justices declined to block other parts of the Texas law during a previous round of litigation.

But pressure is mounting on the high court to address the wave of clinic regulations that have passed in recent years, not just in Texas but also in Mississippi, Alabama, Oklahoma and a number of other states. If the Supreme Court were to hear legal challenges to any of those laws, it would spark the most significant ruling on abortion access since Planned Parenthood v. Casey, the 1992 case that upheld the constitutional right to abortion but cleared the way for state regulation. The key question for the court will be what, exactly, constitutes an “undue burden” on women’s rights.

With abortion access increasingly fragmented, reproductive rights advocates and abortion opponents both want the Supreme Court to weigh in. Stephanie Toti, senior counsel at the Center for Reproductive Rights, told Politico, “the issues in this case are ripe for Supreme Court review.”

In her decision allowing enforcement of the Texas law to go forward, George W. Bush appointee Jennifer Elrod made a point of mentioning that lower courts had issued conflicting decision on the numerous clinic regulations, something that the Supreme Court considers when deciding whether a case warrants their attention. Highlighting disagreement among circuit courts, writes Ian Millhiser at ThinkProgess, amounts to “a blood-red howler to the Supreme Court telling them to “TAKE THIS CASE!”

If it does, the rights of American women will be in the hands of one man.