Mark Mazzetti and Maggie Haberman in the N.Y. Times review the available information on this matter. The election law angle, in my view, is how in the future to protect the Twelfth Amendment joint session in Congress from the risk of mob violence when there is fear that the National Guard, or other forces at the command of the incumbent president, might be put to partisan purposes. This article explains why the Defense Department was hesitant to have the National Guard deployed at the Capitol:

“... The president did tell advisers in the days before Jan. 6, 2021, that he wanted a National Guard presence, but it appeared he wanted the troops as extra protection for his supporters, his aides have privately acknowledged. …

… Law enforcement and military officials planning for Jan. 6 thought that proactively mobilizing the National Guard was a bad idea. The image of armed troops surrounding the Capitol, they believed, was incongruous with a ceremony cementing a peaceful transfer of power.

Gen. James C. McConville, the Army chief of staff, told a Defense Department inspector general investigation in November 2021 that “many people talked about the optics of having military at the Capitol. What that would look like, how that would influence even some of the demonstrators or protesters.”

Christopher C. Miller, the acting defense secretary, was more blunt, saying “there was absolutely no way” he was going to put U.S. forces at the Capitol. He was conscious of news articles that Mr. Trump’s advisers were pushing him to declare martial law and invalidate the election results, he told the inspector general investigation, and having troops at the Capitol might fuel suspicion that he was trying to aid a coup.“

The danger that a president will misuse the military in connection with the counting of electoral votes is not confined to the situation in which the president is an incumbent running for reelection, although obviously that’s the specific circumstance in which the president has a direct personal interest. The president also has a partisan interest in the outcome of the election even when not a candidate. In this regard, it’s instructive to consider how President Grant handled his role in the Hayes-Tilden dispute and, to lesser extent, how President Clinton handled his role in Bush v. Gore (also President Eisenhower in Kennedy-Nixon). Somewhat related is President Lincoln’s role in the consequential congressional elections of 1862, an episode I also address in Ballot Battles because Lincoln’s consideration of the deployment of troops at the Capitol in that context (a move he didn’t need to make once his party prevailed in the organization of the House) raises disturbing questions about how Congress can protect itself against potentially inappropriate presidential interference when Congress undertakes its constitutionally designated role of settling the outcome of an election.

If it is too dangerous for Congress to rely upon the Executive in this context, does Congress have adequate security forces of its own to protect against mob violence? Obviously it did not on January 6, in large part of President Trump’s own adversarial behavior. The work of the House January 6 select committee hopefully will point the way to a remedy.