At the hearing, a lawyer for the president, William S. Consovoy, made it clear that Mr. Trump was likely to raise challenges to the scope of the subpoena, which Mr. Consovoy characterized as “widely overbroad,” and to raise the question of whether there was a political motivation in issuing it.
After the Supreme Court ruling was handed down last week, the White House press secretary, Kayleigh McEnany, called the subpoena “frivolous and politically motivated.”
Mr. Consovoy also said the president should be able to learn more about the district attorney’s investigation, which largely has been kept secret, and that it was unfair for him to have to challenge a subpoena without having access to “at least some information about its nature and scope.”
At the hearing, Judge Marrero noted that in his ruling last year rejecting the president’s claim of immunity, he also found that the district attorney was not acting in bad faith.
In arguing that the delay could prevent a grand jury from considering evidence before any statutes of limitations ran out, Mr. Dunne said that the president was effectively getting the immunity from criminal inquiry that the Supreme Court denied him. Other people and entities could also escape scrutiny, Mr. Dunne said, without elaboration.
Mr. Trump’s lawyers must outline their new objections to the subpoena by July 27, and Mr. Vance can then respond.
Mr. Vance has been looking into hush-money payments that Michael D. Cohen, the president’s lawyer and former fixer, made in 2016 to Stormy Daniels, an adult film actress who said she had an affair with Mr. Trump. The president has denied an affair.