It depends on how much time you want to invest. Some of the missions and dragons are randomly generated so you could literally spend 100's of hours playing. I have heard of a couple people doing the minimum possible to finish the game and still playing for more than 30 hours.
It will depend on how good you are in playing the game. There are people who take a day to beat Skyrim. There are other people who can take 3 days or a week. You have to be really used into playing this game for you to beat Skyrim.
Well, I beat the main quest in less than a week. I did a few side quests, but mostly stuck to the main quest line. This is because I felt bad about just abandoning the mission and the people would be like, "Where is she?" So, with the help of Meeko and Lydia, I finished the who thing as a level 13. I had no problems at all, and only died a few times. I'd say its impossible to do it in a day, however, probably at least 30 hours. It was very fun and addictive!