Some legal analysts are suggesting that the justices of the U.S. Supreme Court will refuse to hear former President Donald Trump's presidential immunity defense to the criminal charges that have been brought against him in Washington, D.C.

Among these analysts is CNN's Ellie Honig.

This regards the so-called election interference case that Special Counsel Jack Smith, on behalf of the Biden administration, has brought against Trump.

Smith claims that Trump committed various crimes when he attempted to challenge the results of the 2020 presidential election.

Trump has pled "not guilty" to the charges, and he is attempting to invoke the doctrine of presidential immunity as a defense.

The general idea of the doctrine is that it protects a president from being prosecuted for official actions taken while president.

The specifics of the doctrine, however, have yet to be worked out by the American legal system, which is why there is some uncertainty about whether the doctrine really does apply in Trump's case.

Trump's presidential immunity defense has already been rejected by the district court and, most recently, by a three-judge panel of the appellate court. It is likely not irrelevant that both courts lean heavily to the political left.

It is expected that Trump will appeal the latest ruling. The only question is whether he will ask the entire appellate court to review the matter before petitioning the Supreme Court. The answer, at the time of this writing, remains unclear.

Honig believes that there is a chance that the justices of the Supreme Court would reject such a petition from Trump.

"The Supreme Court doesn't like to get involved in political cases. You can feel that they weren't thrilled to be involved in the Colorado [ballot removal] case the other day. I don't think they're going to be thrilled about getting involved in this one," Honig said.

He further argued that the Supreme Court may reject the case because there have been consistent rulings at the district and appellate court levels.

These arguments, of course, are not the most convincing. The district and appellate court rulings, for example, may indeed be consistent, but they could be consistently wrong. Also, the magnitude of the case and the novelty of the claim could be considered reasons for the justices to take the case.

It should be noted that, were Trump to petition the Supreme Court to hear his appeal, only four members of the Supreme Court would have to vote in favor of taking the case for the justices to hear Trump's appeal.