In reply to tony:
> Investigate National Park passes - when I was there, you could get a pass for all the parks which worked out considerably cheaper than individual entry (assuming you want to go to the NPs, which, frankly, you should do). >
Its called an America The Beautiful pass, they don't seem to advertise them much so ask for one at the entrance to the first national park you visit. It costs $80 so you'll save money even if you only visit 3 parks (there are 5 all worth visiting) and you can use it for national monuments as well but not state parks. It will also get you discount in some (though not all) national park campgrounds.
https://www.nps.gov/planyourvisit/passes.htm
Try Happy Tours for car hire, I found them about 25-30% cheaper than all the ones you've heard of (including all the comparison sites) when I was over there last summer. They also include full collision damage waiver with no excess and free 2nd driver which you often have to pay extra for which makes them cheaper still.
http://www.happytoursusa.com/en/index.php
That said, its still going to cost you close on £3,000 for 3 months, but between 2 people that's perhaps not so bad? Bear in mind once you're there fuel is dirt cheap and camping/cooking food is cheap. The car and flights are the only big costs.
Also only hire the cheapest budget car. In 7 trips to the US I've always been upgraded and so has everybody else I know, the smallest car I've ever had was a Ford Focus. In fact at the airport the rental cars were parked up in rows according to size, the smallest row was labelled medium, they didn't actually have any small cars.
One final tip, you usually pay a premium to collect your car from the airport, check out the cost at non airport locations. The cost saving could be worth the extra hassle if you're there for that long.