Hasn't the US Military always had this ability? NCIS, CID, etc? These are law enforcement agencies of the various military branches, staffed by civilians, but under orders of the military. They can arrest civilians.
I think the general public would be stunned if they knew what powers the President of the US has. The president has what's called "Executive Orders" that pretty much gives him unlimited power. If you have any doubt about this, check out
Executive Order 9066. Some of the Executive Orders are really out there, such as taking over all transportation in the US and all communication.