If you drove every day, it's only about 2.25 hours/day of driving. I don't think you'll have any problems traveling the distances and seeing the highlights. Of course, it's impossible to see everything as you could travel this route for several years and still not have time for everything. But if you prioritize, you'll be fine.

I always think it's a good idea to have a goal point at the end of each week so you know if you're getting behind schedule or running in front of it. In other words, it's just as bad to be behind and have to rush at the end as it is to get ahead of yourself and find you have lots of time at the end of your trip, thus realizing you could have seen more at the beginning.

I'm a bit concerned about your budget. You might check out this post for ideas on how to determine your budget. Of course, you'll need to add in the cost of your rental car.

I like Michael's suggestion of reversing your route so you're more likely to have access to the northern places at the end of your trip. Definitely visit Yellowstone. There's a reason it's the most visited national park. You'll see stuff there that is out of this world.