On the "Insurrection Act of 1807"…
Congressional recognition of the power of the President to call forth the armed forces to suppress an insurrection first appeared in the Militia Act of 1792.
The Militia Act permitted the President to call forth the militia in response to “an insurrection in any state, against the government thereof” upon the application of the legislature of the state, or of the executive (when the legislature cannot be convened).
The language of the Act of 1807, followed a less specific Act passed by the 7th Congress in 1803, its statements have within, the potential for judicial challenge.
While the prior Act of 1803, as with the Military Act of 1792, which clearly lays out that the Executive indeed has the power to deploy, it seems to have been made moar generic in statement in the 1807 Act.
Moving forward in time…
The act resurfaced in late summer 2005 with the Hurricane Katrina landfalls.
Changes were made in October of 2006 to provide explicit examples of situations that may lead to events of public disorder justifying the President’s invocation of the Act’s authority.
In addition, political and historical limitations, along with limitations in the Act itself, will restrict presidential abuse of the power.
Thus, the uproar over the recent changes to the Insurrection Act and the fears of martial law are unfounded.
The bottom line: The Executive has, thru existing law, the power to deploy! Thus far, as in the case of the Bush Admin, for political reasons, the Act hasn't been enacted.