The Constitution gives Congress the power to call out the militia to suppress insurrections, not the President.
Doing so, however, would be an acknowledgement that a Civil War was in progress, and be likely to provoke a reciprocal response.
The Constitutional also makes the President Commander in Chief. As such, he is responsible for defending the United States.
Consider an American Citizen flying an airliner inbound towards the White House who proclaims his intent to crash that airliner into that building. Do you believe the President could order that airliner shot down?