You should be able to do a lot without really rushing. You do need to realize doing and seeing it all would be more in terms of weeks, or even months, and not days.
We've got close to 200 days logged in since 1986 without even leaving WDW property and there are still things we haven't seen or done. Of course, we see many favorites again each time we go back, but there's always something new and something changed. We simply have something to look forward to in the future. We also do not rush anymore. You'd be surprised how different it is when you take your time.
Basically, you need a day each at the Magic Kingdom, Disney Studios, and Animal Kingdom and two days at Epcot for all the basics. That should leave you plenty of time to see other things, relax a bit and still have some time to go back to a few of the parks for things you missed.
Hope you have a wonderful trip!