Adam Kinzinger, one of two Republican members on January 6 committee, on Sunday vowed to “get to the bottom” of events surrounding the 2021 insurrection at the US Capitol but refused to reveal whether the panel intends to question Ginni Thomas – wife of US supreme court justice Clarence Thomas – over reports of her urging the White House to overturn Donald Trump’s election defeat.

Senior Democratic Senator Amy Klobuchar said Clarence Thomas must recuse himself from relevant cases and warned the integrity of the supreme court is at stake.

Kinzinger refused to confirm or deny the existence of text messages Ginni Thomas is reported to have exchanged with then White House chief of staff Mark Meadows, although he did not contest the Washington Post and CBS’s joint revelation last week that they obtained copies of such messages from materials submitted to the congressional committee by Meadows.

“The question for the committee in this or any exchange is ‘was there a conspiracy, or how close did we get to overturning the election?’” he told CBS’s Face the Nation show on Sunday.

Kinzinger, one of two Republicans on the House select committee investigating the events surrounding 6 January 2021, said of witnesses being summoned to give evidence to the committee: “We’ll call in whoever we need to call in.”

He added: “Was there an effort to overturn the legitimate election of the United States? What was January 6 in relation to that? And what is the rot in our system that led to that and does it still exist today?…We are going to get to the bottom of this.”

He did not say whether that “rot” extended to the nation’s highest court.

Thomas and her husband are rightwing political darlings who have described themselves as “one being – an amalgam,” according to the New York Times.

Amid the latest reports, Justice Thomas is now facing calls to recuse himself from any cases surrounding the 2020 presidential election, the insurrection and potentially the 2024 presidential election, should Trump run for re-election.

Meanwhile Klobuchar of Minnesota, chairwoman of the Senate rules committee and a member of the Senate judiciary committee, which quizzes nominees for the supreme court, demanded that Clarence Thomas be removed from any such cases.

“This is unbelievable,” Klobuchar told ABC’s This Week. “You have the wife of a sitting supreme court justice advocating for an insurrection, advocating for overturning a legal election, to the sitting president’s chief of staff. And she also knows this election, these cases, are going to come before her husband. This is a textbook case for removing him, recusing him, from these decisions.”

The 29 exchanges reported between Ginni Thomas and Meadows reveal how the wife of one of the land’s top jurists disseminated disinformation related to the QAnon conspiracy theory and other inaccurate arguments during the tempestuous days following the November 2020 election when right-wingers were claiming Democrat Joe Biden had not won.

Even as Trump strategized efforts to overturn his defeat through the courts, Virginia “Ginni” Thomas “spread false theories, commented on cable news segments and advocated with urgency and fervor that the president and his team take action to reverse the outcome of the election,” the Post reported.

It reported she wrote to Meadows: “Help This Great President stand firm, Mark!!!…You are the leader, with him, who is standing for America’s constitutional governance at the precipice. The majority knows Biden and the Left is attempting the greatest Heist of our History.”

Pressed about how he and his colleagues would broach Thomas’s alleged attempts to undermine a legitimate US election, Kinzinger said they want to ensure their work is “not driven by a political motivation, it’s driven by facts”.

The House select committee has so far hesitated to demand cooperation from Thomas in part because they are worried she may “create a political spectacle to distract from the investigation”, the Guardian previously reported.

Klobuchar said: “All I hear is silence from the supreme court right now. And that better change in the coming week because every other federal judge in the country except supreme court justices would have guidance from ethics rules that says you got to recuse. The entire integrity of the court is on the line here.”