A Democratic member of the Judiciary Committee, Senator Chris Coons of Delaware, agreed with Mr. Graham that Mr. McCabe’s remarks “deserve scrutiny.” But he took issue with Mr. Graham’s characterization of the situation.

“I don’t think that this frankly rises to the level of some deep state conspiracy or a serious attempt at what Senator Graham called an administrative coup,” said Mr. Coons, also speaking on “Face the Nation.” “I suspect that once this is fully discussed, it’ll be clearer that this was a brief or passing conversation that’s been taken out of context.”

Mr. McCabe made the explosive remarks in an interview with the CBS program “60 Minutes,” released in part on Thursday, in advance of its full airing Sunday evening. He said Justice Department officials became so alarmed by Mr. Trump’s decision in May 2017 to fire James B. Comey, the bureau’s director, that they discussed whether to recruit cabinet members to invoke the 25th Amendment, which outlines the succession plan should the president become incapacitated, resign or die in office.

In a second clip of the interview aired Sunday on “Face the Nation,” Mr. McCabe said he spoke to the president just after Mr. Comey was fired, and subsequently ordered the bureau’s team investigating Russia’s election interference to look into whether Mr. Trump had obstructed justice by firing Mr. Comey. The F.B.I. also began examining whether Mr. Trump had been working on behalf of Russia against American interests.

Mr. McCabe said that he and others were “concerned about a national security threat.”

He continued: “And the idea is, if the president committed obstruction of justice, fired the director of the F.B.I. to negatively impact or to shut down our investigation of Russia’s malign activity and possibly in support of his campaign, as a counterintelligence investigator you have to ask yourself, ‘Why would a president of the United States do that?’”