House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffOvernight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) said the committee is considering subpoenaing former national security adviser John Bolton John BoltonDiplomacy with China is good for America The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep DOJ launches probe into Bolton book for possible classified information disclosures MORE as impeachment moves to the Senate.

Schiff said on CBS’s “Face The Nation” that bringing Bolton in for testimony in the lower chamber is an option but added that there is “little sense” in having Bolton testify in front of the House but not the Senate.

“If they’re going to be the triers, and in fact they will be, they should hear from the witness directly. He has offered to come forward and testify,” he said. “There is no reason not to have him come forward and testify unless you just want to cover up the president’s wrongdoing.”

NEWS: .@RepAdamSchiff tells @margbrennan that the House Intelligence committee is “considering” subpoenaing John Bolton, who has previously said he would testify if subpoenaed in the Senate. pic.twitter.com/pUkXGLqdoh — Face The Nation (@FaceTheNation) January 12, 2020

Schiff said the U.S. will see a “fair trial” for the president and the American people. He added that if Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) is successful in stopping other witnesses from testifying, the trial would be a “sham” and a “cover-up.”

“And I think one of the things that holding on to the articles has succeeded doing is fleshing out McConnell and the president’s desire to make this a cover-up,” he said.

Speaker Nancy Pelosi Nancy PelosiMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Pelosi must go — the House is in dire need of new leadership MORE (D-Calif.) told ABC’s “This Week” that it was a possibility the House would subpoena Bolton or submit new articles of impeachment but added, “Let’s just see what the Senate does.”

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Schiff's and Pelosi's comments come after Bolton expressed a willingness to testify in front of the Senate if subpoenaed. McConnell has argued against agreeing to have witnesses and additional documentation in the Senate trial before hearing opening statements.

The House impeached the president for abuse of power and obstruction of Congress last month, moving the matter to a Senate trial. But Pelosi has not sent the articles to the upper chamber yet.

The Speaker said she would withhold the articles until she learns the Senate’s rules for President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE’s trial but has indicated she will pass them along as early as this week.