But he could utilize 10 USC § 253, Interference with State and Federal Law, which is part of the Insurrection Act and 10 USC § 252, Use of Militia and Armed Forces to Enforce Federal Authority.
The authority is vested solely in the President. He does not need the invitation of state governors to intervene, nor does he need the approval of the Supreme Court. Older provisions of the Insurrection Act required either a governor or a judicial proceeding to authorize its use, but these limits were purposefully removed by Congress in § 253.
There is no time limit on the President’s activities. Older versions of the Insurrection Act limited the use of force to brief periods of time and then required legislative approval. Those limits, too, are also gone. The President is allowed to use any means that he (and again, he needs no one else) considers necessary. This includes using the armed forces (which enables him to bypass the Posse Comitatus Act) and using the militia which is detailed in 10 USC § 252 " Use of Militia and Armed Forces to Enforce Federal Authority."
The President’s ability to use force isn’t restricted to actual rebellion or insurgency. He can act against merely unlawful combinations and conspiracies. To be clear: If the President decides that a conspiracy has deprived people of a right and believes that authorities fail or refuse to protect the right, he can send in the troops.
In blunt terms, Congress has given the power to President Trump to proclaim:
“I, President Trump, have determined that a conspiracy has deprived 70 million Americans of their right to vote and that the other authorities are refusing to protect this right. I therefore order the suppression of this conspiracy by any means necessary.”
And to your other comment about the date, there are still methods within the constitution about counting the electors and certifying them that may help Trump before the January 20th date. I'm not even sure the Jan. 20th date is hard and fast. At least one president in our history wasn't determined and sworn in until March.
And then what?
The President does not have the power to reverse the decision of the Electoral College or order a new election, etc.
And January 20 is a set date - it's not going to change not can the President change it. Sections 3 / 4/ 5 of the Amendment allow for addressing the situation of the president-elect, etc dying before taking office, etc.