is there enough to see and do in staying in the city of Vienna for 1 week?
If you go and it everything to you that you dreamed it would be, then yes. If it turns out to rub you the wrong way, and that can happen to good, smart and well traveled people, then its way too much.
If its your only destination in Europe, then with the cost of getting there and back, make it work and find enjoyment at all cost.
If you are stopping in a second city like Prague or Budapest and you have cut the second to 3 days so you can have a week in Vienna, then a week may be too long.
If you are looking at day trips to use time not because they facinate you, then it may be too long.
Budget might play into it as well. It's a bit pricy.
As Emily pointed out a major portion of Vienna's tourist sights are a modern reconstruction. Most go, some multiple times, and never realize it.
It took me a while to warm up to the city, but I enjoy now and living only a few hours away I never turn down an opportunity to visit. And I could spend a week.