Manhattan District Attorney Cyrus Vance Jr. heralded the U.S. Supreme Court's 7-2 ruling Thursday that President Donald Trump is not immune from state criminal subpoenas as a "tremendous victory," but some hurdles remain before a New York County grand jury can obtain Trump's tax returns.

"Those who think the DA's office is on the verge of indicting Donald Trump or his business, I think that seems premature," said Harry Sandick, a partner at Patterson Belknap Webb & Tyler and a former assistant U.S. attorney in the Southern District of New York.

Barring a leak from the grand jury, the ruling is also unlikely to result in the public release of Trump's tax returns prior to the November election, experts agreed Thursday.

Attorneys for Vance, Trump and the president's accounting firm Mazars will likely appear next before their trial judge, U.S. District Senior Judge Victor Marrero of the Southern District of New York.

Chief Justice John Roberts' opinion said the president can "challenge the subpoena as an attempt to influence the performance of his official duties, in violation of the Supremacy Clause," which opened the door for Trump to make new arguments in the lower courts, David Rudenstine, a constitutional law professor at the Yeshiva University Benjamin N. Cardozo School of Law, said.

"It's not clear to me what the president would actually argue to make out a persuasive claim that performance of the subpoena would interfere with his Article II duties, but his lawyers may very well have some things in mind," Rudenstine said.

The case could be appealed again to the U.S. Court of Appeals for the Second Circuit, and Rudenstine said it's "very possible" that there will be no compliance with the subpoena prior to the election.

Sandick estimated that the process could take months. If the federal judges again agree with Vance and the grand jury obtains the tax documents before the November presidential election, they would still be protected by the usual secrecy of a grand jury proceeding.

"I think if you're in Vance's office, you want to be on the phone, basically, today, with the lawyers for the financial institutions and also the Trump lawyers and say, 'When are our documents coming?' and try to force this to move quickly," Sandick said.

Even if the grand jury receives the documents and decides to indict someone associated with the president, criminal defense lawyer and former Manhattan assistant district attorney Mark Bederow noted that the documents will not necessarily become public anytime soon.

"It's not commonplace that after there's an indictment, a prosecutor dumps all the evidence in the public domain just for the sake of doing so," he said. "There has to be a reason that that information would be released."

Many details about the investigation are unknown, Bederow said, adding that the grand jury proceedings could also be slowed down by the ongoing coronavirus pandemic.

"We don't know what they're investigating, don't know how far along they are in investigating that, don't know how complex it is, if it could take several months, as sometimes very sophisticated white-collar investigations may do," he said.

In a tweet Wednesday morning, Trump's attorney, Jay Sekulow, confirmed that the presidential legal team will continue to raise objections in the lower courts.

"We are pleased that in the decisions issued today, the Supreme Court has temporarily blocked both Congress and New York prosecutors from obtaining the president's financial records," Sekulow said. "We will now proceed to raise additional constitutional and legal issues in the lower courts."

In a statement, Vance emphasized that the grand jury has already waited many months for the documents. Trump sued Vance and the accounting firm Mazars USA in September, one month after the DA's office subpoenaed eight years of Trump's tax returns and assorted other financial information related to the president, his businesses and his associates.

"This is a tremendous victory for our nation's system of justice and its founding principle that no one—not even a president—is above the law," Vance said. "Our investigation, which was delayed for almost a year by this lawsuit, will resume, guided as always by the grand jury's solemn obligation to follow the law and the facts, wherever they may lead."

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