The US Department of Defense is one of the only organizations that takes a strategic look at the effects of climate change, and they are flat-out in a tizzy about it. (Side-glance to KB, for links to evidence...)
I fully expect, that before I die - sometime in the next 40 years - that I will have fortified my home, and will have strangers living in my yard.
They may be people from Phoenix, or Nevada, or Mexico, or Central American countries. But they will be there, because their homes became uninhabitable due to drought, weather, food, dust-bowl conditions, etc. They had to leave, to survive.
The migrant caravans will move north, ignoring borders and laws. Because when millions of people come walking into your town, the police are going to be entirely powerless against them. (CUT TO: scene of Walking Dead zombies shambling towards the camera)
Phoenix has no plan for when it runs out of water, in a couple of years.
LA's power infrastructure can't support sustained periods of 113 degrees, like they had this year.
Normal people cannot survive without the support of a fully-functioning city... flushing toilets, on-demand water from the tap, police and health services, food, etc. So the Climate Migrants won't be moving to the Sierra Nevadas and national parks and setting up Little House On The Prairie-kinds of existences, because they don't have the skills.
They will move to the big cities. Who are already taxed to the limit, and can't sustain an influx of hundreds of thousands of people. So a few will stay (couple of million), and the rest will continue on the road.
The Great American Migrant Caravan.
In my lifetime. I'll bet on it.