As President Donald Trump stood idly by with violent protestors ransacking the U.S. Capitol on Wednesday, at least two of his top officials and closest allies conferred with staff about the possibility of invoking the 25th Amendment.Secretary of State Mike Pompeo and Treasury Secretary Steven Mnuchin held informal conversations within their own agencies about the contours of the 25th Amendment, the invocation of which would begin a process to remove Trump from office, according to three sources familiar with the matter.The arguments against pursuing action, according to the three sources, were manifold. First, the legal process itself was estimated to take more than a week, negating any immediate effect it would have. Second, it was unclear whether the three secretaries serving in “acting” roles without Senate confirmation would be able to cast a vote. Third, they had concerns that forcing Trump from office could further stoke tensions among his base and make him a hero of the far right, doing more bad in the long-term than good in the short-term. “The general plan now is to let the clock run out,” said one former senior administration official aware of the discussions. “There will be a reckoning for this president, but it doesn’t need to happen in the next 13 days.” Mnuchin, traveling overseas, declined to comment. A State Department official denied the conversations took place. A current senior administration official said Pompeo may have been gathering information in preparation for a Cabinet discussion, even if he himself was not willing to personally lead the effort. “The first oath the secretary ever took was at West Point, and that oath was to the Constitution,” this official told CNBC. Secretary of State Mike Pompeo and Treasury Secretary Steve Mnuchin speak during a briefing on terrorism financing at the White House Tuesday, Sept. 10, 2019, in Washington.Alex Brandon | APBeyond the exploratory conversations among the secretaries and their staffs, there was no formal advancement of the effort. Other Cabinet secretaries noted they had not been contacted about potential meetings to discuss the issue. “I’ve had no contact with other Cabinet members in that area, nor do I expect to have any,” Agriculture Secretary Sonny Perdue told reporters at a gaggle in Georgia, where he once served as governor and where he spent recent days campaigning for his cousin, Sen. David Perdue. “I know some people have issued their resignations, which as I mentioned, is their prerogative.” The number of administration officials resigning from the Administration grew on Thursday. They include deputy national security adviser Matt Pottinger and White House chief economist Tyler Goodspeed. Mick Mulvaney, former acting chief of staff now serving as Special Envoy to Northern Ireland, said on CNBC he couldn’t stomach continuing to serve, even in a part-time diplomatic post. “I can’t stay here. Not after yesterday,” Mulvaney said on CNBC’s “Squawk Box.” “You can’t look at that yesterday, and think I want to be a part of that in any way, shape or form.” Other officials are choosing to stay on — at least temporarily — to try to ensure a smooth transition to the next administration. Chris Liddell, the deputy chief of staff for policy coordination, has decided to stay in his role leading the transition to the new administration, according to another senior administration official. Transportation secretary Elaine Chao, who in her resignation letter said she was “deeply troubled” by the actions of the president’s supporters, is not leaving the agency until Monday. A source familiar with her plans says she had a previously scheduled meeting with the team of Secretary-designate Pete Buttigieg and did not want to leave that in the hands of other officials. Subscribe to CNBC on YouTube.