I would doubt that you could do this trip properly on 3k on your own. You are going to pay a hefty price for such a long one way rental for a start and nobody to split the cost with. T then do it over a few months, I can't see it happening. I have driven your route on two separate trips but both with the same start and end point. My latest was up around Seattle - it was circa 2k per person and that's based on 2 sharing so half price hotel rooms, car hire, gas etc.
Either think about how you arrange the trip, ie perhaps go for less time and find a friend to do it with and use the same start and end point, or save the trip until you have more funds.
If you want to just go away and travel for 2 months on 3k then don't do the USA, take people's advice and look at Asia instead, your money will go much further.