They would definitely shrink, but they would still be around. Look at Medicare, they have supplement polices which the individual has to pay. If you think the government is going to pay for Heart surgery, Cancer treatment, you're in for a rude awakening. Please check this out ca medical term http://funadvice.com/r/btfucae9o4m. It might be helpful.
I'm sure the government will still have it so that the insurance companies will continue to get rich :)
In progress....we are all about to see what happens....