There is nothing in the Insurrection Act (that people are talking about) that allows the President or any president to set up an extra-Constitutional government.
Here is the text of the law.
https://www.law.cornell.edu/uscode/text/10/252
"Whenever the President considers that unlawful obstructions, combinations, or assemblages, or rebellion against the authority of the United States, make it impracticable to enforce the laws of the United States in any State by the ordinary course of judicial proceedings, he may call into Federal service such of the militia of any State, and use such of the armed forces, as he considers necessary to enforce those laws or to suppress the rebellion."
Eisenhower invoked it to enforce the Supreme Court's desegregation rulings, and Lincoln used it as the legal basis for going to war against the South.
But like all laws (and the Insurrection Act is a law), it is subject to the Constitution and the courts.
Lincoln did away with habeas corpus, and he had no legal or Constitutional right to do so.
Now, having said that, there could be something in this declaring of a "National Emergency" - but God knows what that entails, because I certainly don't.
The President cannot setup an extra-constitutional government.
There are some FReepers that have alluded to invoking the Insurrection Act gives the Presidents control over the Federal Legislature and Judiciary. They're sadly mistaken.
The President can't do away with or shutdown those institutions. There's no law that could give that authority as it would not be superior to the US Constitution.
That FReepers have been calling for mass arrests, martial law, etc is very telling.
President Trump will not invoke any law or declaration that will 1) lead to martial law 2) contravene the US Constitution regarding the election of the President. No doubt if he did, the House would vote to impeach with Republican support and the Senate would note to convict with substantial Republican support.
President Trump is not a tyrant - I wish FReepers would stop yearning for him to become one.