Portions of a Texas law that would dramatically reduce access to abortion are on hold, thanks to an order that the U.S. Supreme Court issued late Tuesday. And while it's not clear whether the reprieve is temporary or permanent, the Court's action ought to make abortion rights advocates feel at least a little more optimistic.

The law is the infamous clinic “safety” measure that Governor Rick Perry signed last year. It requires, among other things, that all abortion providers use facilities that meet the formal facility standards of “ambulatory surgery centers” and that physicians who work at such clinics have admitting privileges at nearby hospitals. Abortion rights advocates have warned that as few as seven abortion providers would remain open if the new standards take effect—and that, as a result, about one-sixth of the population would be at least 150 miles away from the nearest provider. Prominent physicians and organizations representing the medical establishment have said, repeatedly, that such requirements are not necessary for patient safety. (Read Jen Gunter’s QED story about this if you want more background.)

Abortion rights advocates filed a lawsuit challenging the Texas statute, citing prevailing legal doctrine that recognizes a woman’s right to get an abortion without “undue burden.” In August, a federal district judge declared the law unconstitutional, but earlier this month, a three-judge panel of the Fifth Circuit Court of Appeals essentially overruled the district judge and said that Texas officials could begin enforcing the new requirements. Now the Supreme Court has stepped in and wiped away (part of) that Circuit ruling, by issuing an order of its own. At least for the moment, Texas officials can’t enforce the new law and the clinics can stay open.

The legal saga will continue. First, that three-judge panel from the Fifth Circuit must actually rule on the merits of the lawsuit challenging the Texas law. They will most likely reject the suit and uphold the law. (Why else would they have blocked the district ruling from taking effect?) Once that happens, abortion rights advocates will ask the Supreme Court to take the case and the Court will probably agree.

And then? The order doesn’t say which justices voted in favor of it. But the list almost certainly included the four liberals and it probably included Anthony Kennedy, who has been the key swing vote on abortion cases. He has been the fifth vote to invalidate some restrictions (like the spousal notification requirements in Planned Parenthood v. Casey) and he has been the fifth vote to uphold others (like the partial-birth abortion ban in Gonzales v. Carhart.) If he voted in favor of Tuesday’s order, as seems likely, that could mean he thinks the restrictions in the Texas law go too far and violate a woman’s right to abortion. There’s even a possibility that Chief Justice John Roberts has doubts about the law, because the order mentions that Justices Samuel Alito, Antonin Scalia, and Clarence Thomas would have allowed the Texas law to take effect. It says nothing about Roberts.