(CNN)The Trump White House deputy chief of staff Dan Scavino has a deadline next Thursday to respond to the House Select Committee's subpoena for documents related to January 6 and has another deadline the following week to testify -- but his attorney Stanley Brand says he's not ready to cooperate.

       The new details about Scavino's House subpoena emerge as committee members from both parties attempt to play hardball to entice witnesses to testify about January 6 and former President Donald Trump, and give new hints as to how that push may become bogged down in legal strategy.

       Scavino retained Brand to help him respond to the House investigation a few days ago, and on Tuesday his legal team called the committee on a main phone line. Brand heard back Wednesday afternoon, with the committee giving Scavino additional time to respond to his subpoenas, according to the lawyer and a source familiar with the committee's deliberations.

       Substantive negotiations haven't begun, and Brand said his client might not comply with subpoena deadlines until then.

       Earlier Wednesday, Brand complained the committee wasn't engaging with him.

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       "Not having heard anything, I don't know what to say" about whether Scavino will defy the subpoena, Brand told CNN on Wednesday. "They have to act like a real investigative entity."

       Regarding the document request, Scavino doesn't have many records to turn over personally because his communications as a White House official are now held by the National Archives, Brand said.

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       The committee's requests for topics Scavino might know about "are as broad as the ocean," Brand added.

       Scavino has legal concerns about testifying, Brand added, including whether the committee properly served him his subpoena and how unsettled executive privilege issues, which Trump raised in a lawsuit this week, might be dealt with during an interview.

       So far, the Biden White House hasn't asserted executive privilege over the January 6 White House records nor to block witnesses sought by the House, and Brand said the current White House counsel's office hasn't been in touch with him.

       The House Committee is moving forward to hold Trump ally Steve Bannon, who didn't work in the government on January 6, in criminal contempt and plans to ask the Justice Department to prosecute him. Committee members have made similar threats of contempt prosecutions toward Scavino and others they've subpoenaed.

       The committee has postponed scheduled depositions with Mark Meadows, former chief of staff in the Trump White House, and Kash Patel, a former Defense Department official, while negotiations continue.

       Brand believes ex-officials like Scavino may be able to hold off the committee from pursuing criminal contempt, because of valid legal arguments they can make.

       A prosecution isn't guaranteed even if the House makes a referral to DOJ, and the contempt charge would also have to survive a judge and a jury's scrutiny for a conviction.

       The current standoff with the House is "not beanbag," Brand said, invoking a favorite phrase of Washingtonians condemning political antics.

       "This is not a political game. This is a serious legal issue," Brand, a former House general counsel, said.