I suppose Article IV Section 4 could give cover to states to use the militia as a local police:
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
-PJ
That section would probably apply to an insurrection that is too big for the state to handle. A decent militia ought to be able to handle an insurrection.