It depends on your touring style. If you only want to hit the highlights ( a few rides/shows) at each park, and have an express pass, you can do it in a day. If you want to do it all at each park and have an ep, you can do one day in each park- so a total of two days. If you want to do it all, and are a repeat rider family, three to four days with ep should do it.
We are a repeat rider type of family, and like to tour at our leisure, not commando a park. Usually 3-4 days is good for us, and we have even stayed for a week before, only leaving one day for an outing to SeaWorld. And we were not bored.
So one day just really is not enough to do a park justice unless it is a really slow day.
Let's put it this way. Many people think WDW is just for kids, we know better. In the same way, UO is more than just a thrill park, it is a beautifully themed destination in and of itself with many details and shops and restaurants to enjoy.
Just depends on what you want to get out of your UO experience.