I think saying you could do it easily on $2000 is a little unrealistic. You have to be really committed to being cheap to do that. Not saying you can't, but you're not going to be showering very much, not eating in restaurants at all, not drinking any alcohol, not staying in a hotel even if the weather is really horrible or you're sick, etc.
Note that if you are solo it is more expensive per person, because you can't split the cost of lodging (camp sites & hotels). Also, food can be a bit more expensive solo, because it's pretty hard to cook a healthy varied meal for yourself and not end up with leftovers that you can't use - so you end up either cooking really boring stuff with only a few ingredients, carrying leftover items which may spoil before you eat them, or eating out a bit more.
3 months is probably a little more than most people take.
Everyone is different. $2000 is about what I spent and it was probably a bit less. I am naturally frugal, but did not feel like I pinched pennies much on that trip. I think I only drank alcohol twice on the trip (a beer with a meal). No I didn't stay in motels much (one night we paid and one night a friend put us up), but I did eat in restaurants a good bit (usually second breakfast or lunch). There were three of us sharing expenses and sometimes we saved by splitting expenses, but more than half of the time we stayed for free. In addition when we did pay a good portion of the time it was priced per person. So we saved a little by being in a group of three, but I don't think it was all that much.
Additionally there were places we could have cut costs further. The $2000 included things like shopping at the Patagonia outlet and having stuff sent home, buying some clothing and gear along the way, stopping in tourist traps like the "Sea Lion Cave", a night in a cabin, a night in a tee pee, several stops at expensive KOA style campgrounds, and a day of whitewater rafting.
On the other hand we probably got more invites to stay with folks than I would have gotten if I was alone. People assumed we were a father and two daughters and I think that made us very approachable.
All that said it is a good idea to allow plenty of extra, just in case. I had allowed $5000, but still had $2500 in the account at the end. Bear in mind that airfare, a car rental, a night's motel stay before we started the tour, and a day of sightseeing in Newport before the trip all came out of the $5000 in addition to all daily spending during the tour.
Bottom line... For me I could see doing the trip for as little as $1500 without being a complete cheapskate or as much as $3000 depending on what the trip was like. If I went at a good clip, didn't do a lot of tourist stuff, and pinched my pennies I think my daily expenses (not counting airfare etc.) could be as little as $1500. If I took my time and did more tourist stuff I can imagine it being as much as $3000.
I agree that 3 months is at the longer end of the range and that it would mean higher trip cost because of more meals and campsite fees.