if you continue to drive they will shoot you inside your car.
There's n crime against doing that; you may be charged with resisting or even evading but there's no crime like 'Ramming a police vehicle' or 'Aggressive use of a motor vehicle' etc.
Also yeah it is legal in the US to some degree. If a protestor (or robber, thug, fugitive etc) goes up to your car and starts attacking you or your vehicle, threatening you with a gun knife etc; you are legally within your bounds to flee in whatever means possible, even if it includes running over the guy.
Played GTA, if you point a gun at someone through their windshield they are gonna run your ass down!