The House January 6 committee could subpoena Ginni Thomas, the wife of the supreme court justice Clarence Thomas, if she will not testify voluntarily about her involvement in Donald Trump’s attempt to overturn the 2020 election.

The news, from panel member Liz Cheney, came two days after Trump’s former strategist, Steve Bannon, was convicted of criminal contempt of Congress for refusing to cooperate with the committee. He faces time in jail.

On Sunday the second Republican on the committee, Adam Kinzinger, said, “You can’t ignore a congressional subpoena or you’ll pay the price”, a warning he said applied to “any future witnesses too”.

Cheney, vice-chair of the panel, told CNN’s State of the Union: “The committee is engaged with [Ginni Thomas’s] counsel. We certainly hope that she will agree to come in voluntarily but the committee is fully prepared to contemplate a subpoena if she does not.”

Thomas corresponded with Mark Meadows, Trump’s chief of staff, and John Eastman, a law professor who shaped the congressional side of a push which culminated in the deadly Capitol attack.

She also corresponded with Arizona Republicans about attempts to overturn Joe Biden’s victory there.

Her activities have added to pressure on her husband. The arch-conservative was the only justice to say Trump should not have to release records to the House committee. His wife’s communications with the Trump camp were subsequently revealed.

Some on the left have called for Thomas to be impeached – a political non-starter.

Cheney said: “I hope it doesn’t get to [a subpoena]. I hope [Ginni Thomas] will come in voluntarily. We’ve certainly spoken with numbers of people who are similarly situated in terms of the discussions that she was having … so it’s very important for us to speak with her.”

Bannon was convicted after the committee made a criminal referral to the Department of Justice but in Meadows’ case, the DoJ declined to pursue charges.

Kinzinger told ABC’s This Week those who defy subpoenas should face ‘justice, right? Come in, you can plead the fifth if you want in front of our committee but you can’t ignore a congressional subpoena or you’ll pay the price.”

He added: “That’s to any future witnesses too.”

Elaine Luria, the Virginia Democrat who with Kinzinger presented the committee’s case in a hearing on Thursday, told NBC’s Meet the Press: “I don’t think [the DoJ] can revisit something that they’ve already dismissed but [Meadows is] certainly someone who has probably more information than anyone, you know, other than the folks who we have already heard from who were in the White House that day.”

She added: “If he’s listening, we’d love to hear from him.”

Kinzinger has said he thinks the panel has proved Trump broke the law in his attempts to overturn the election. Cheney would not go so far.

She said: “I think that Donald Trump’s violation of his oath of office, the violation of the constitution that he engaged in, is the most serious misconduct of any president in the history of our nation.

“The committee has not decided yet whether or not we’ll make criminal referrals … I would also say that the Department of Justice certainly is very focused, based on what we see publicly, on what is the largest criminal investigation in American history.

“But there’s no doubt in my mind that the former president of the United States is unfit for further office.”

Luria said: “I sure as hell hope [the DoJ has] a criminal investigation at this point into Donald Trump.”

She also said Merrick Garland, the attorney general, “has already told us he’s listening, and if he’s watching today, I’d tell him he doesn’t need to wait on us because I think he has plenty to keep moving forward.”

The House committee has held nine hearings, eight in a summer run which ended on Thursday with almost three hours on Trump’s inaction while the Capitol was attacked. There will be more hearings in September. Cheney said more interviews were scheduled and the committee “anticipate[s] talking to additional members of the president’s cabinet. We anticipate talking to additional members of his campaign.

“Certainly we’re very focused as well on the Secret Service.”

The deletion of Secret Service text messages from 5 and 6 January 2021 despite an order from the committee to preserve them is another flashpoint.

Cheney praised witnesses including Cassidy Hutchinson, a former aide to Meadows, and Sarah Matthews, a former White House press aide.

Cheney said: “Certainly it is the case that the attacks against some of the women witnesses have been particularly vicious. I also think the response that we’ve seen from the House Republicans is really disgraceful.

“… I think our country is at a moment where we really have to all of us take a big step back and say, ‘Look, the normal, sort of vitriolic, toxic partisanship has got to stop and we have to recognise what’s at stake.’ And … the leadership of the Republicans in the House need to be held accountable for their actions.”

Cheney is expected to lose her seat in Wyoming over her opposition to Trump. She would not be fully drawn on whether she plans to run for the Republican presidential nomination in 2024, when Trump is expected to do so.

“I’ve not made a decision about 2024,” Cheney said, “and I am really very focused on the substance of what we have to do on the select committee, very focused on the work that I have to do to represent the people of Wyoming. And I’ll make a decision about 2024 down the road.

“But I do think as we look towards the next presidential election … I believe that our nation stands on the edge of an abyss. And I do believe that we all have to really think very seriously about the dangers we face and the threats we face and we have to elect serious candidates.”