If your total budget is only around $3000 US, my suggestion would be to forget it. If your departure point to go back home is the same as your arrival point and you really are planning to drive say, from Florida to California to Washington state and back to Florida, your gasoline costs alone will be around $1700. That's not leaving much for paying for the vehicle itself, let alone food and normal travel expenses.
I just finished a trip from New York to Sacramento; roughly 2700 miles one way and gas was around $600. Granted, I'm driving a pickup that's getting around 19 mpg on the highway, but still...an RV would get half that in gas mileage.
Work out a budget for a per day cost of around $30/day for food, tolls and the small stuff, and a 2 month trip with just that is $1800.
It's a REALLY big country. Your best bet may be to select two or three states to visit and rent a van, as has been said. Keep in mind that most rental car companies that rent vans will charge mileage as well, sometimes as much as $.40 a mile. The advantage to renting a car would be unlimited miles for the duration, and you should be able to get monthly rental rates around $600/month for a midsized car. A minivan may be a good option, but the cost would probably go up to around $800/month.
Keep in mind that the least expensive areas to live in and visit in the US are down south (mostly) and the midwest. The Pacific Northwest could be very good, too.
If your flight is not set, and you have a very open itinerary, the least expensive airports I've ever rented a car in (and yes, it was for two months) was Columbus, Ohio and New Orleans, LA. Flying into either of those cities and staying within 700 miles of them would give you a really nice slice of Americana, with the history of the Mississippi river all along the way.
I hope this helps, if you make it out to California (Sacramento) and need a place to crash and rest up for a day or two, let me know. If I'm home, you're more than welcome.