The federal judge overseeing former President Trump's federal 2020 election trial officially postponed its March 4 start date indefinitely while his claim of presidential immunity remains on appeal.

Why it matters: It's now likely that the first of Trump's four criminal trials will be over New York's charges related to 2016 hush money payments, which is slated for March 25.

Judge Tanya Chutkan did not set a new date.

The expected delay in the federal 2020 election case could also push the trial closer to the November elections and could set back others, including the trial over classified documents that's set for May 20.

Catch up fast: The Jan. 6 case was paused in December while Trump appealed a lower-court's rejection of his immunity claims.

Special prosecutor Jack Smith attempted to prevent the delay by asking the Supreme Court to weigh in on whether Trump is protected by presidential immunity.

It rejected the request, meaning Trump's appeal must first get through the U.S. Circuit Court of Appeals for D.C. before the Supreme Court can decide if it will take up the case.