At that point in time, constitutionally, the president has the authority to order the House and Senate to disregard all illegal EC votes from contested states.
Invoke the Insurrection Act and the courts will toss it out in a matter of days. But if Trump wants to declare martial law then he can toss the Electoral College, the courts, the Congress, and remain in office as long as he wishes.
January 6 will be a very interesting day.
If Trump invokes the insurrection act on January 5, 2021 at 11:50 pm, then the Democrats can’t stop the insurrection act by January 6, 2021 because courts will not act until the Democrats prove to the court that Trump has been served with the legal papers of their lawsuit first. All Trump has to do is refused to be served. January 6, 2021 will come and go without any Democrat’s attempt to block the insurrection act.