Many hundreds of couples have been married there in the last week. Judge Robert J. Shelby of Federal District Court in Salt Lake City turned back a request to stay his decision, and a two-judge panel of the United States Court of Appeals for the Tenth Circuit, in Denver, agreed, though it called for “expedited consideration” of the appeal.

The question for the Supreme Court in the short term will be whether to block Judge Shelby’s ruling while appeals proceed. The state’s request will initially be directed to Justice Sonia Sotomayor, the member of the court responsible for overseeing the Tenth Circuit, but she will almost certainly refer the matter to the full court. It is likely to act within several days.

The Supreme Court will face difficult calculations, ones it did not have to confront in reviewing decisions from federal courts in California striking down Proposition 8, the state’s ban on same-sex marriage. In that case, the United States Court of Appeals for the Ninth Circuit, in San Francisco, stayed both the trial judge’s ruling and its own as appeals went ahead.

Professor Dorf said there are probably not five votes on the Supreme Court to block Judge Shelby’s ruling. “On the strictly legal argument,” he said, “it’s hard to justify granting a stay.”

But he added that the lower courts should have done so, partly because of the potential cruelty of voiding the new marriages and partly because the Supreme Court is hard to predict.

“It’s pretty clear that even the five justices who are sympathetic to same-sex marriage would rather take a few years before getting there,” Professor Dorf wrote in a blog post on Tuesday. “If their hand is forced, as it now will be, it’s impossible to say with certainty what they’ll do.”

Whatever the Supreme Court does regarding a stay, it is hard to see how it could hear the larger issue in the case in the current term. But a decision in the court’s next term, culminating in a decision in June 2015, is entirely possible.