If you can bring the money to the table, probably 1 million at least, either money out of your pocket or a sponsor, and you are a very talented driver, you could probably join an existing team to drive with for a season. Getting in for the 12hr race would be pushing it as far as time constraints go.
If you have the time and money to dedicate to training yourself you MAY be able to do this on your own before the 12 hour race, but you'll basically need to have several days a week free, every week, up until the race. I would imagine this should consist of doing driver schools (Panoz, Skip Barber) at the most advanced levels they are offered, and then probably entering some club races on your own.
Cost of the schools, flights, hotels, car to race with, etc? $100,000 when all i said and done sounds reasonable. Realistically if this was going to happen you would have needed to get started 6 months ago, trying to squeeze all this in now sounds to me to be pretty much impossible