The stay appeal will be made to Justice Sonia Sotomayor, who is assigned oversight of the 10th Circuit Court of Appeals.
The state's previous four requests for a stay were denied once by the U.S. District Judge Robert J. Shelby, who ruled Dec. 20 that Utah's ban on same-sex marriage was unconstitutional, and three times by two 10th Circuit judges.
If Sotomayor, appointed to the bench in 2009 by President Barack Obama, makes the decision on her own, either side could seek a different opinion from the entire court. She also could decide to refer the stay application to the entire court, said Carl Tobias, a professor at the University of Richmond School of Law, who specializes in federal court issues and constitutional law.
"The tradition and the practice in this kind of a case, which I would consider to be high-profile and relatively controversial, is that justices tend to refer it over to the whole court," he said. "It's [the notion] that nine heads might be better than one on that kind of case."
In his view, odds are against the state.
"You've had one district judge and two 10th Circuit judges look at the stay question and resolve it against the state of Utah," he said. "To some extent, there may be deference from the Supreme Court on that. I think it's hard to reverse three judges. The more stays that are denied, the more difficult it becomes."
That's the case even more so if Sotomayor, 59, handles it on her own and also denies Utah's stay application.
"If she denies it, I would be shocked if the whole court reverses," Tobias said. "My reading of the order out of the 10th Circuit was that Utah's arguments weren't that strong. I just think it's unlikely to be granted."
In its third denial order, the 10th Circuit noted that of four required criteria for granting a stay two are "most critical:" likelihood of success on appeal and threat of irreparable harm if a stay is not granted.
"They require more than a mere possibility of success and irreparable harm," the 10th Circuit said, adding that based on the parties' arguments, "a stay is not warranted."
Legal observers describe Sotomayor as one of four liberal judges on the Supreme Court. In Tobias' opinion, Sotomayor was "favorably inclined to same-sex marriage" in the two most recent cases that came before the court Prop 8 and DOMA.
"But they were not the same issues," Tobias said.
She sided with the majority in the United States v. Windsor case, which overturned the federal Defense of Marriage Act.
When the court declined for technical reasons to rule on the Proposition 8 case this summer thus leaving gay marriage legal in California Sotomayor joined Justice Anthony Kennedy, Clarence Thomas and Samuel Alito in the dissent. That is, in her opinion the proponents of Proposition 8 who brought the suit did have standing to defend their interests even if the state chose not to act.
During oral arguments she observed that, "The assumption is that there are not executive officials who want to defend the law. They don't like it. No one's going to do that. So how do you get the law defended in that situation?"
Whether Sotomayor reviews the stay request on her own or refers it to all the justices, the decision is likely to come quickly, Tobias said.
"Every day clerk's offices in Utah are open, hundreds of people are being married," he said. "The state has always thought time was of the essence, and the justices are likely to agree and move very quickly once the papers are in."
Likewise, the 10th Circuit has agreed to hear the appeal of Shelby's decision on an expedited basis, which means the entire process likely will take "a couple months," Tobias said. And while that court's ruling on Utah's stay request is a "bit of a signal," it "doesn't tell you how the merits [of the case] are going to come out."
In other words, stay tuned.