The cap on state taxes could have a serious effect on the price of real estate here in NH. This is because NH does not have a income OR sales tax. Instead we have very high property taxes. For example, the local property taxes on my single family residence is $8K. This is for a house that is currently worth about $340K. I know many upper middle class people whose property taxes are in excess of $10K here in NH. However, NH continues to be one of the lowest overall tax burden states in the country.
We're paying about $9K here in the People's Republic on a house that's maybe worth $400K (Zillow says $500K. They gotta be kiddin'!) My late FIL's place -- 10 x the size and closer to the water -- had a $40K tax bill and that was 10 years ago. The problem here in the People's Republic is that everything else - income, sales, inheritance, business -- is taxed to the max, too.
My thought is that I doubt that NH real estate would be hurt too much. In Massachusetts -- one of the Seven Deadly (tax) States, it would. It's the overall tax burden, not any one single tax source.
The high tax states are in trouble. Mostly what the tax bill would do is make them advertise that fact. But I don't think it's going to happen.