Following Supreme Court ruling, what happens next in Trump's criminal hush money case?

With Donald Trump's sentencing in his New York hush money case delayed until September following Tuesday's decision by Judge Juan Merchan, the judge now faces the task of applying the Supreme Court's new test for the limits of presidential immunity to the former president's criminal conviction.

Trump in May was found guilty on 34 felony counts of falsifying business records related to a 2016 hush money payment to adult film actress Stormy Daniels in order to boost his electoral prospects in the 2016 presidential election.

Trump's lawyers have argued that the judge should "set aside" the jury's verdict in the case because the jury heard evidence during the trial that would have been protected by presidential immunity, based on Monday's ruling by the Supreme Court that Trump is entitled to "at least presumptive immunity" from criminal prosecution for official acts taken while in office.

To rule on the defense's request -- which Judge Merchan plans to do by Sept. 6 -- he will likely have to answer two key questions, according to former federal prosecutor Jarrod Schaeffer.

The first question is, would the Supreme Court's decision have limited some of the evidence and testimony at trial?

Rather than argue that Trump's conduct related to Daniels' hush money payment constituted official acts of the presidency -- an argument a federal judge rejected last year -- Trump's lawyers have focused on what they have called "official-acts evidence."

Evidence including Trump's social media posts in 2018, a government ethics disclosure, and phone records were cited as examples of evidence related to official acts that prosecutors emphasized during their closing arguments to the jury.

Prosecutors introduced some of Trump's tweets about his former lawyer Michael Cohen to emphasize what they called a "pressure campaign" to prevent him from cooperating with investigators in 2018.

"Michael is a businessman for his own account/lawyer who I have always liked & respected. Most people will flip if the Government lets them out of trouble, even if it means lying or making up stories," Trump wrote in an April 2018 tweet.

The Supreme Court's decision on immunity included some protections for Trump's communications -- including tweets -- because they "fall comfortably within the outer perimeter of his official responsibilities"; however, the ruling added that lower courts would need to determine if Trump was speaking in his official capacity as president or in an unofficial function such as a candidate for office or party leader.

Merchan declined to consider Trump's last-minute challenge to some evidence, including the tweets, ahead of trial, determining that Trump's request to exclude the evidence was "untimely."

Defense lawyers also suggested that some testimony from Trump's former White House communications director Hope Hicks would have been protected by immunity.

"I think Mr. Trump's opinion was it was better to be dealing with it now, and that it would have been bad to have that story come out before the election," Hicks testified during the trial regarding a 2018 conversation with then-President Trump about Stormy Daniels' accusation of a long-denied 2006 sexual encounter with Trump.

Prosecutor Joshua Steinglass later described that testimony to the jury as "devastating," saying that it "puts the nail in Mr. Trump's coffin."

According to Schaeffer, Hicks' testimony poses a novel question to Merchan, who will need to weigh the Supreme Court's limit on using "testimony or private records of the President or his advisers" as evidence at trial.

"Even if these are conversations about unofficial acts or purely private conduct, the President is having these conversations with official advisers or people who perform an official role in connection with the presidency," Schaeffer said. "Would intruding on these conversations or allowing these records to be used cause the next president to hesitate before having these kinds of candid conversations with people that they need to rely on in order to execute their duties?"

In addition to prohibiting prosecution for official acts of a president, the Supreme Court's ruling restricted the use of evidence related to official acts in cases related to a president's private actions, including limiting evidence and testimony from a president's advisers.

According to Justin Levitt, a constitutional law professor at Loyola Law School, the ambiguity of the Supreme Court's decision about the use of such evidence presents an opportunity for Trump's lawyers, despite a federal judge already determining that the hush money payment was "purely a personal item of the President."

"It's not entirely clear what they meant by the prohibition on the use of evidence," Levitt said. "For as long and prominent an opinion as it was, it's not very careful, and so it doesn't provide a lot of guidance."

Schaeffer said the second question Merchan will have to consider is, did the jury rely on that evidence and testimony when it reached a guilty verdict?

If Merchan determines that the evidence cited by prosecutors was protected by presidential immunity, he then needs to weight if the introduction of the evidence at trial was harmless or if it created a "structural error that rendered this trial utterly unfair," according to Schaeffer.

"I don't know the answer to that," said Schaeffer. "I don't know that anyone does, because I'm not sure that I've seen a situation where the Supreme Court has eliminated an entire class of otherwise permissible evidence from a prosecution after a trial has taken place and before sentencing."

Some experts suggested that the evidence highlighted by Trump in a March pretrial motion -- such as tweets about Cohen -- were unlikely to have influenced the verdict.

"There's just a mountain of other evidence that would support the jury's verdict, so I don't see it really having any appreciable impact, if any impact, on the New York case," Pace University School of Law professor Bennett L. Gershman told ABC News.

However, prosecutors themselves placed emphasis on Hicks' testimony when urging jurors to convict the former president -- potentially creating an issue if the testimony is deemed to be protected by immunity.

"She basically burst into tears a few minutes -- a few seconds after that because she realized how much this testimony puts the nail in Mr. Trump's coffin," Steinglass said in his closing arguments to jurors about Hicks' testimony.

If Merchan opts to set aside the verdict, he could order a new trial without any of the contested evidence related to official acts, according to Levitt.