The growing controversy raises fresh questions over the role of Barr, the attorney general who has been criticized as a partisan Trump loyalist.
Tapper asked Swalwell, who sits on the Judiciary Committee, if the House would impeach Trump over the Stone's case.
Donald Trump praised his attorney general William Barr for recommending a more lenient sentence for his former adviser Roger Stone on Wednesday, just hours after the move prompted all the prosecutors in the case to resign.
Democrats plan to ask Barr about the department's decision to overrule four federal prosecutors on the amount of prison time recommended for Stone.
Now the president is attacking the judge overseeing the case on Twitter.
Speaking to reporters later at the White House, Trump thanked Justice Department officials for retracting the prison term recommendation.
During her press conference, Pelosi added that Barr's actions had "deeply damaged the rule of law" and said that the Stone interference, plus Trump's abrupt firing of impeachment witnesses, must be "investigated".
Stone's conduct before the court after he was indicted, which included posting on Instagram a photo of Judge Jackson with a symbol that appeared to be crosshairs next to her head, was also cited as an aggravating factor in the original sentencing recommendation.
News broke Tuesday that the Justice Department had overrruled the sentencing recommendation.
Trump on Tuesday criticized US prosecutors who recommended a prison sentence of seven to nine years for Stone in connection with his conviction in a case stemming from former Special Counsel Robert Mueller's investigation detailing Russian interference in the 2016 election to benefit Trump's candidacy.
Last year Mr Barr was widely criticised for claiming that special counsel Robert Mueller's Russian Federation investigation had exonerated Mr Trump, when in fact the final report outlined several instances in which the president may have obstructed justice.
"In our criminal justice system, a single standard must apply to all who are accused or convicted of violating the law-unequal treatment based on political influence is to be deplored in all cases but is especially unsafe if it emanates from the presidency". He is due to be sentenced on February 20. He also assisted in the case against former Trump campaign chairman Paul Manafort.
Barr told ABC that he hoped the President would react and respect the criticism of his tweets delivered in the interview.
"The Justice Department's mission "to ensure fair and impartial justice for all Americans" requires that its prosecutorial decisions remain free from political influence", all ten Democrats on the committee, led by Ranking Member Dianne Feinstein, wrote in a letter to Graham on Thursday.