On its face, Judge Furman’s order only enforces a court rule governing changes of legal counsel. Practically, however, it presents the department with a difficult choice: Either reverse course and leave its old legal team in place, or produce sworn explanations that could prove both embarrassing and damaging to the administration’s case.

The department’s legal campaign had already undergone head-snapping changes in strategy this month. Department lawyers first said they were abandoning the case in the face of a Supreme Court ruling blocking the question, only to reverse course the next day, after President Trump called their statement “fake” and said the case would continue. They then told a federal judge that the administration was exploring a “legally available path” to restoring the question.

But that handed opponents of the citizenship question a legal opening: In a motion in Judge Furman’s court last week, they argued that the government had repeatedly said the lawsuit had to be resolved by June 30, when the printing of the 2020 census forms had to begin. The department’s announcement that it would continue to press for the question in July belied that explanation, opposition lawyers said.

They also suggested that the administration had set a false deadline for resolving the case to keep opponents from uncovering evidence that the citizenship question had been driven by a desire to help the Republican Party gain power when census figures are used to draw new political boundaries in 2021. The challengers said they would pursue sanctions against the defense for its conduct.

The Justice Department announced the switch in legal teams two days later on Sunday. While the department has not explained the change, multiple people familiar with the case have said that the lawyers resigned from the lawsuit out of ethical concerns and a belief that the suit was unwinnable.

Those people have said that many of the lawyers did not see a path forward on the case, given that any argument they made could appear to contradict statements to district judges and to the Supreme Court that the administration had to have a decision by June 30. Just as important, they faced a conflict of interest in trying to represent a client — the President of the United States — who had just publicly branded them liars.