Lawyer Charles Burnham revealed the remarkable information in a letter to panel chair Rep. Bennie Thompson (D-Miss.), in a week that marked another Trump loyalist, former DOJ official Jeffrey Clark, suggesting he intended to take the Fifth.
"Dr. Eastman hereby asserts his Fifth Amendment right not to be a witness against himself in response to your subpoena," Burnham wrote.
"Dr. Eastman has a more than reasonable fear that any statements he makes pursuant to this subpoena will be used in an attempt to mount a criminal investigation against him," wrote Burnham.
Burnham goes on to describe a few complaints with the subpoena itself – including attacking the makeup of the Jan. 6th select committee itself. House Speaker Nancy Pelosi created the body, appointed two-panel Republicans after a fight with Minority Leader Kevin McCarthy over its composition after she rejected his designs.
He said the committee lacks a "ranking minority member," which "makes it impossible to comply with relevant House Rules, including those applicable to subpoenas and depositions."
He also said the subpoena itself is "extraordinarily broad" and "goes far beyond even the most expansive reading of the Committee's authorizing resolution in asking for materials bearing no reasonable relation to the events of January 6."
He mentions an "extreme risk of gross unfairness to the subjects of your investigation," and mentions the decision to take testimony behind closed doors, in a letter received by Politico.
Eastman took part in a Jan. 4th Oval Office meeting where members discussed whether Vice President Mike Pence had the power to not accept votes verified by states that eventually made Joe Biden President when Congress met to include votes Jan. 6th.
Eastman spoke to the Jan. 6th "Save America" rally, and wrote two memos, what he calls a draft and a six-page version, putting out several election cases, including one where Vice President Mike Pence would refuse to verify votes certified by states where Trump was claiming election fraud happened.
He says in his meeting with Trump he advised having Pence move to adjourn a common session of Congress when lawmakers met to count the electoral votes.
Clark showed up for a November statement but refused to be interviewed. Thompson said shortly before the panel's hearing, the committee was alerted that Clark wishes to assert his right against self-incrimination.
"This is, in my view, a last-ditch attempt to delay the Select Committee´s proceedings. However, a Fifth Amendment privilege assertion is a weighty one. Even though Mr. Clark previously had the opportunity to make these claims on the record, the Select Committee will provide him another chance to do so."