Rick Pildes makes the case. I agree with Rick that if the Court takes the case, that’s a nice piece of evidence that the Court does not care about public opinion. But there are many reasons the Court could choose to summarily affirm the case even if they don’t care at all about public opinion. The lower court opinion by Judge Kavanaugh (himself, quite skeptical of campaign finance reform and the author of the Emily’s List opinion) saw the RNC as merely trying to dress up a facial challenge in as applied clothing. The Court, for reasons wholly apart from public opinion, may want a more direct facial challenge to the soft money rules (arguing that this aspect of McConnell too should be overruled) so that the litigants can focus on that question beginning in the lower court, and deal directly with stare decisis issues (something Justice Alito seems especially concerned about).
I have little doubt that if the Court summarily affirms in this case, the RNC would file another case raising just such a facial challenge.