“They have requested a ridiculous amount of documents,” Mr. Nunberg said. “Should I spend 30 hours producing these? I don’t know what they have. They may very well have something on the president. But they are unfairly targeting Roger Stone.”

The subpoena also demands any documents related to Carter Page, a former Trump campaign foreign policy adviser who was secretly surveilled by the Justice Department as part of the Russia investigation, as well as Paul Manafort, the former Trump campaign chairman, and his deputy, Rick Gates. Mr. Manafort has been indicted on a string of money laundering and fraud charges, and Mr. Gates recently pleaded guilty and agreed to cooperate with Mr. Mueller’s investigators.

The list of people about whom Mr. Mueller is seeking information from Mr. Nunberg raises questions about his target, as does the time frame. Mr. Nunberg was fired by Mr. Trump during the summer of 2015 and thus was gone from the campaign in November. And he and Mr. Lewandowski are known to be combatants.

Still, Mr. Nunberg — whose mentor, Mr. Stone, goes by the motto that all press is good press — spent hours on Monday engaged in a media tour with The Times, The Washington Post, CNN and MSNBC, describing his plans to flout the subpoena and professing his lack of concern about what could happen to him.

“I was fired within six weeks” of the campaign’s start, Mr. Nunberg told The Times, despite having “saved” Mr. Trump during a fight with Senator John McCain, Republican of Arizona, that summer after Mr. Trump’s remark that Mr. McCain was not a war hero because he was captured in Vietnam. Mr. McCain was shot down during the war and imprisoned for more than five years in Hanoi, refusing early release even after being beaten repeatedly.