As Jack Balkin at Balkinization points out, the Cheney plan to use the military to arrest terrorists in the United States amounted to a suspension of the Fourth Amendment.
The central problem with the Cheney/Yoo/Addington theory was that it allowed the President to declare anyone in the United States an enemy combatant. Then, once the President made this declaration, the person would lose all their civil rights. The military could arrest and imprison the person without charges or any of the procedural protections of the Bill of Rights; it could torture them for information (under the theory that these techniques did not shock the conscience under the Eighth Amendment), and it could hold them indefinitely in a military prison. The problem with the Cheney/Yoo/Addington theory, in short, was that it embraced elements of military dictatorship within the United States.
Frankly, until Republicans come to terms with this, I really can't see trusting them with executive ranch power again. Ever.