Realistically speaking, what are most refugees in the USA going to do? I'd say ... keep on driving. You can get a long way in a car - provided you've got snacks, water and a full tank of gas. If connecting roads are open, then even a huge herd of refugees can dissipate over a wide area.
So if you want to avoid having a major hassle with these people, all you really need to do ... is to give them access to convenience stores and a gas station. Keep the major streets open - sooner or later they will pass on through.
The only problem is for bedroom communities that are located within walking distance of major cities. If the entire city has a disaster, and for some reason people cannot drive out, then you're going to wind up with a flood of people who walk a few miles. But the good news ... many Americans are obese and they probably won't walk huge distances.
I'd like to hope that human nature is generally good and that most people will assist refugees ... by offering some water or snacks. Try to keep in mind - if a huge number of Americans are really forced to flee - then these people have probably already been through hell.
And I suspect that the folks living in Idaho are pretty safe. Nobody's going to flee that far.
cheers,
other Pete