The case is set to be argued May 12, and briefing was completed weeks ago, so the order from the court caught lawyers by surprise and raised the possibility that the justices were looking for a way to avoid deciding the case's merits.
It may also be less dramatic than that. The request could reflect the interest of just one or a small group of the nine justices.
In the cases, Trump has raised sweeping arguments that the president is protected from investigation by congressional committees and, separately, a New York district attorney. The lower courts are currently considering the power of Congress to demand executive-branch compliance with its investigations.
The court's Monday order applies only to the president's dispute with Congress. It said that Trump's personal lawyers and attorneys for Congress and the Department of Justice "are directed to file supplemental letter briefs addressing whether the political question doctrine or related justiciability principles bear on the court's adjudication of these cases."
The political question doctrine refers to the idea that some disputes must be resolved by the executive and legislative branches, and are not the province of federal courts, which are meant to be apolitical.
It seems likely that all of the lawyers in the Trump cases will argue that the court has a role to play.
The Supreme Court has agreed to consider three cases in which Trump is fighting subpoenas seeking financial records from him and family members, including the income tax documents Trump has declined to release.
One subpoena is from the House Committee on Oversight and Reform and the other involves investigations by the House Committee on Financial Services and the Committee on Intelligence. Both seek records from financial organizations Mazars and Deutsche Bank, rather than from Trump himself.
Manhattan District Attorney Cyrus Vance has requested records for his own investigation into whether alleged hush-money payments made during the 2016 presidential campaign to Stormy Daniels, an adult-film actress, and to former Playboy model Karen McDougal violated state laws. Both women said they had affairs with Trump years ago, something the president denies.
Mazars and Deutsche Bank are not taking part in the lawsuits and say they will abide by court decisions.
Trump's lawyers declined to speculate about the court's order, with Jay Sekulow saying only, "We will respond accordingly."
Some law professors and court observers surmised that the political-question doctrine could give the justices a pass during a particularly intense moment in the battle over the separation of government powers.
It is always "a little problematic to try to read tea leaves" from the Supreme Court, said Brianne Gorod, chief counsel of the liberal Constitutional Accountability Center. But the request could mean that the justices are "looking for a way to avoid deciding this on the record."
Her organization has urged the court to find that Congress has the authority to subpoena the president's financial records. But she said invoking the political question "could be the wrong route to the right decision" if it freed the financial organizations to release the records.