Americans would probably not adapt as quickly as the Iraqis, simply because Iraq has been through this sort of thing before, with Saddam's war against Iran, the Persian Gulf War and the 2003 invasion.
Our populace would probably react much like the Iraqis did, though. They'd be very frightened at first, then they'd become somewhat cavalier, develop gallows humor and deal with it, unpleasant as it is. However, social events like meeting at restaurants or parks would be severely curtailed because the fear would be ever present. People would go to work when they could, get supplies in a very speedy and furtive manner, take care of any pressing business but any unnecessary errands would not be done.
Because of our size and population, there would likely be a civil war.
It's no way to live.
And that has passed here now and the Iraqis are going back to a normal, happy lifestyle.
Heaven forbid that we in the U.S. would ever have to go through what they've been through over the past few years. I pray I never see anything even remotely resembling that in my own country.