I second phates idea. There are plenty of us here across the US and having a strong network of friends will be your best asset. I personally wouldn't mind having company for a night. *edit for spelling errors...
You could probably make the trip across the usa for less than $1000, if you drove day and night, ate & slept on the cheap. Figure around $100 a day for food, gas, lodging (this is assuming you stay in a cheap, $50 hotel, fill up $30 worth of gas once per day, and keep meals to $20.) If you're planning on having any fun (like stopping in Las Vegas or something, staying in a hotels that aren't crapola, etc) then the estimate of around $2000 sounds realistic. Personally I wouldn't drive that far, too much can go wrong - car breaks down, caught in snowstorm, flat tire in Death Valley, caught by a family of cannibalistic rednecks, etc. If you're coming during Dec - Jan be prepared for snowstorms, thunderstorms, etc across the midwest, as well as incredibly bad food and towns with three buildings in them. Best advice I've seen here is probably take a train part of the way, takes less time and costs a lot cheaper. Plus they serve meals on the trains, you can use your laptop and there's real bathrooms. Don't travel by bus, unless you like smelling people's armpits.
Any of the major rental companies will allow you to. I've done it a bunch of times without an issue and with their full knowlegde. Enterprise and Hertz do, at least. Tim, I don't recommend what you plan to do. You'd be better of taking the train and stopping at the major cities on the way. Driving 3k is something to tell the grandkids perhaps, but that is all. Mostly you'd be on the highways which are completely unremarkable and mind numbing. Definitely not recommended. Add to this that most US drivers are more dangerous than in the UK and the violence you might encounter on the road (depending where you stop) and it's just not worth it. A waste of money that you could better spend in much better ways in the USA sightseeing. I doubt he drove across the USA in an $800 car. It's not like Europe. Used cars here hold better value. You'd not want to cross the state in an $800 car, let alone the country.
For the places where you don't have any AG member to take care of you, you can spare money and have a great time hanging out and sleeping at locals by registering at www.couchsurfing.com, creating a profile and contacting people living on the route if they want to hangout and have a place for you to crash. If you need more detail PM me but first if interested read that site carefully.
Ok I think the plan is going to be train/bus to a few places heading south. If anyone wants me to come visit them then PM me with details and I can start making a plan. I'm aiming to leave early/mid december. Been talking to K-Pang and probably going to end up meeting her in Uruguay in January too. All so exciting.
Y al final que mierda pensás hacer?? Thatis uruguayan spanish for asking what the fuck Twimfy's plan is now...
Do you have a general trip plan worked out - may give a heads up to let people know if you will be going through their area.
Should you have to go through Mexico by land instead of air to get to South America, I can offer some advice. Also - I would take the Train idea that Assembler suggested. I think it's safer and cheaper. I really wouldn't like my old P.O.S. car breaking down in the middle of fucking nowhere...
Plan has totally changed now. Heading to Thailand on wednesday and then on to australia, then New Zealand back to Australia again then thailand again and south america at some point in that mix.