Over at Volokh.com, another legal expert, Orin Kerr, argues:

If the Supreme Court agrees to hear the case, I don’t think the factual record will matter very much. I think that for three main reasons. First, the Justices will know that this case presents a defining moment for their respective tenures on the Court. This will be one of the biggest decisions of their careers, and its importance transcends a single trial before a single judge with a particular set of witnesses. These sorts of mega-big-picture cases tend [to] rest less on the details of the factual record than other cases. Second, the Justices will certainly recognize. . . Judge Walker was trying to use his facts to make an argument designed to persuade the Justices to agree with him. For better or worse, I suspect a majority of the Justices will respond to that dynamic by significantly discounting those facts.

“Finally, a majority of the Court had relatively harsh language about Judge Walker’s rulings on broadcasting the trial when it took the remarkable step of overturning his order back in January. This passage at the end of the Supreme Court’s per curiam opinion stands out:

The District Court attempted to change its rules at the eleventh hour to treat this case differently than other trials in the district. Not only did it ignore the federal statute that establishes the procedures by which its rules may be amended, its express purpose was to broadcast a high-profile trial that would include witness testimony about a contentious issue. If courts are to require that others follow regular procedures, courts must do so as well.

That’s not the kind of language that suggests that a majority of the Justices will be overly inclined to defer to the Judge’s factual findings in the resulting trial.

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