I don't believe that Muslims are an inferior people, so I tend to think that they would react like anyone else... Southerns after Sherman, for example.
And considering that your scenario didn't pan out then, why would it pan out now?
War is hell... and as long as civilians are sheltered from that hell, they'll work for and call for war. Expose them to it and all the talk goes out the window.
Furthermore, wars only ever really end when one side is thoroughly shown to be defeated. When the citizenry are made to realize that they really did lose, then there no mistaken belief that the losing side could have really won, for the evidence against it is all around.
Just look at Germany and Japan after WWII. Cities in rubble, starvation, and massive internal displacement. There was no way the German/Japanese citizenry was going to claim that the allies simply used dirty tricks to occupy their country. Unlike what we see with our nice, sanitized, 'precise' wars of today.
Well, perhaps, but it is a brutal method for winning. I would prefer to protect our own borders and society much, much more thoroughly, crack down hard on the actual terrorists we find, and largely ignore what Muslim civilians may be doing in their own lands (in *our* lands is a totally different thing though).
The situation in the South is different, though. The Federal government still directly controls the South. I hope to God the U.S. government doesn’t directly control Iraq and Afghanistan a century and a half from now. Also, let’s face it, there is still resentment in the South over this even though it’s been so long since it happened. National reconciliation could have been much smoother if this particular military tactic hadn’t been used. Remember too the destruction was so great in general during the war that the South was left impoverished for a century after the war (there were, of course, several causes for this, but I think the facts indicate that the war’s extraordinary destruction and death was the most important one).