Looming over the latest disruptions was a July 1 deadline to begin printing 2020 census materials — a deadline that the Justice Department said could not be stretched without imperiling the schedule for the census itself.

Since Mr. Ross tacked the citizenship question onto the census in March 2018, long after other aspects of the questionnaire had been settled, the Census Bureau has been at the center of a ferocious partisan battle over the 2020 head count, its carefully tended reputation for trustworthiness and political impartiality all but shredded.

An army of critics, from cities and states to ethnic and civil-rights advocates, have argued that the question is an ill-disguised effort to skew the census’s results to the benefit of the Republican Party. That was only reinforced by the disclosure last month of a 2015 study by a Republican strategist, Thomas B. Hofeller, that explained how data from a citizenship question could be used to exclude noncitizens from the population bases used in redistricting. The newly drawn districts, he wrote, would tilt toward non-Hispanic whites and Republicans and hobble representation of Hispanics and Democrats.

Mr. Hofeller, who died last year, was the first person to urge Mr. Trump’s transition team in 2016 to add the question to the 2020 head count. Three separate federal courts — in New York, Maryland and California — have ruled that the Commerce Department violated federal procedural law and the Constitution in tacking the question onto the census. They called the department’s rationale — to improve enforcement of the Voting Rights Act — an obvious cover for some other motive.

On Wednesday, Judge Hazel ratcheted up the pressure on the administration to make up its mind, ordering the Trump administration either to confirm by Friday afternoon that it was not placing the citizenship question on the census questionnaire, or offer a schedule for continuing the Maryland lawsuit.

“Given that tomorrow is the Fourth of July and the difficulty of assembling people from all over the place, is it possible that we could do this on Monday?” Mr. Gardner asked.