Honestly I have a bit of a skewed perspective having worked there in the summers of 2009 and 2010. I wouldn't want to go unless I had at least a week to devote to visiting the park but a lot of it depends on what you want to do there. If you're into backpacking a weekend won't cut it. If you're just going to drive up to the viewpoints then you can get by with just a couple of days.
Additionally, if you're able to cross into Canada, the Waterton Park across the border (The combined parks are called Waterton-Glacier International Peace Park) is stunning as well. And if you really have some time to mess around in CA, Banff National Park is only about 3 hours away just outside Calgary.
Must See in GNP if you go (off the top of my head):
If you are into more than just basic trail hiking I highly recommend the Climber's Guide. It'll tell you exactly how to get wherever you want to go in the park and how difficult it is.
My favorite book on hiking is Glacier is Climber's Guide to Glacier National Park by J. Gordon Edwards. Even if you're not into technical climbing, it's an excellent guide for some great hikes and scrambles away from the crowds.
A Climber’s Guide to Glacier National Park by J Gordon Edwards. 14 hikes later, created a foundation such that the rest is history.