Yes, the Internet will put local car dealers out of business – at least the new car dealers. People are very aware of the need to save money nowadays. No one wants to pay any more than they absolutely have to and expensive purchases like cars are well researched. More people are realizing they can purchase a new car on the Internet for sometimes several thousand dollars less than they would pay at a dealership. There is no salesman’s commission and no mark-up. As more people become aware of this, they will start realizing they really don’t want to part with that much money unnecessarily at a dealership.
As long as local car dealers continue to provide services that the Internet doesn't (and, currently, can't) like the ability to actually go there and see what you're buying and try it out, there will be an advantage to having actual local car dealers. Of course, they will probably integrate themselves with the Internet, like having a web site, but this relationship is one of them using the Internet, not being put out of business.
I do not believe that the internet will put local car dealers out of business because certain people prefer to do their business face to face, rather than on the internet. Also, local car dealers can use the internet to boost their businesses, by developing their own websites and advertising online.
I come from a small town where we have 2 local used car dealers and one that sells brand new and used cars. My family and I have always physically went to a local dealership and test drove vehicles and made an informed decision about what we saw in person. I think that's always important to go support local businesses and get a "feel" for the products being offered. The internet is convenient, but you may not always get what you think!