I think the American government would send secret agents with the power to use any means necessary after her. Much like the Alliance.
Given the US gov't couldn't even get away with far less during the Cold War without catching political hell (the Church Committee, for example, or Iran-Contra), I don't think any U.S. President would be foolish enough to send out hencmen with the ability to do ANYTHING, particularly to US citizens. Look at all the trouble the Jose Padilla case caused and he was ultimately convicted of a crime by a jury of his peers.
(plus there'd be major inter-agency problems--how do you know some police officer in Peoria isn't going to mistake said agent for a kidnapper or terrorist and shoot him? It would be hilarious if the Operative was undone, not by Mal or any of the heroes, but some redneck cop who thinks the guy is a psycho killer.)
At least inside US borders. OUTSIDE US borders, a lot can be gotten away with in the name of fighting terrorism.
This gets into the matter of separation of powers in the Alliance. If the Alliance is a unitary state, orders to all local police to cooperate with the Operative could go out. If it's a federal system like the US, you'd have to hash it out with state, local, etc, and that's far more doable.
And if the Feds are capable of dispatching agents with unlimited power, how come Michael Moore and other gadflies are still alive? The temptation to use them to settle scores with domestic political opponents would likely be overwhelming.