NORTH TEXAS (CBSDFW.COM/CNN) – The 5th US Circuit Court of Appeals in New Orleans is holding a January 7 hearing on what should come next in abortion clinics’ federal lawsuit challenging Texas’ six-week abortion ban — a lawsuit that the Supreme Court kept narrowly alive in a decision handed down last month.

The legal issues before the 5th Circuit are extremely technical. But at stake is whether abortion providers will have any shot in the coming months to get an order that would at least partially block enforcement of the law.

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The clinics have already asked the Supreme Court to intervene yet again in the 5th Circuit’s handling of the case. So far, the justices have not taken any action on that request, which was filed Monday night.

For more than four months, a law that bans a majority of abortions in the country’s second most populous state has been in effect. Given the legal risks that come with violating the ban, which outlaws abortions when fetal cardiac activity is detected, clinics have been unwilling to offer the procedure in those instances — a point around six weeks into the pregnancy, before many women even realize they’re pregnant.

The pace at which the proceedings have moved since the Supreme Court handed down its decision shows just why abortion clinics were so disappointed in the ruling. They quickly asked the Supreme Court to expedite the next steps in the case and send it immediately back to Judge Robert Pitman, the district court judge who briefly blocked the law last fall. Instead, Supreme Court Justice Neil Gorsuch, who wrote the court’s majority opinion, sent the case back to the 5th Circuit, which had frozen the moves by Pitman to block the law’s enforcement.

Clinics have asked the 5th Circuit to send the case back to Pitman. But instead, the appellate court is hearing oral arguments on a request by the state and other defenders of the six-week ban to send the case to the Texas state Supreme Court.

In the background of these procedural maneuverings is an even bigger threat to abortion rights not just in Texas — but nationwide.

The Supreme Court last month heard a separate abortion case out of Mississippi that gives the conservative majority the opportunity to gut — and perhaps, outright reverse — current precedent protecting abortion access before the fetus is viable, or can survive outside the womb. So far, the Texas ban has been allowed to stand in the face of that precedent because of its unique enforcement mechanism. Rather than impose criminal or administrative penalties for clinics that conduct abortions after six weeks, the Texas law allows private citizens to sue those providers — or anyone else who assists the person obtaining the abortion — in state court, with the threat of damages of at least $10,000.

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In its decision in the Texas case last month, the Supreme Court said that the clinics’ lawsuit challenging the ban could move forward against a narrow set of state licensing officials. Now, Texas wants its state Supreme Court to review the role those licensing officials play in enforcing the ban, and whether, under state law, the challengers can move forward with some aspects of the federal court proceedings against those officials.

Texas has also asked the 5th Circuit to set a briefing schedule for other procedural issues in the case that, according to the ban’s defenders, were left unresolved by the US Supreme Court’s recent decision.

Legal observers have noted it was an extremely rare move for the 5th Circuit to schedule oral arguments on Texas’ state supreme court certification request.

The 5th Circuit panel’s lone Democratic-appointee — Judge Stephen Higginson — said in a dissent that the panel’s majority was adding “impermissible delay to the vindication of the constitutional rights of Texas women in federal court.” The other members of the panel are Judges Edith Jones and Kyle Duncan.

While abortion has remained inaccessible in Texas for people more than six weeks into their pregnancies, those who have the means to do so are flooding out of state clinics, the providers said in their most recent filing with the US Supreme Court.

“And the rush of Texans fleeing to seek care is causing weeks-long appointment backlogs in other States, harming residents of multiple States and invariably delaying first-trimester abortion patients across the country until later in pregnancy,” the providers said.

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