Do you need a constant internet connection to play Portal 2?

You actually don't need internet to play the game by yourself. If you were to play with a friend, then you would need constant internet, but otherwise, you shouldn't have to at all. Try to unplug your internet completely from your laptop/PC and then running the game. It should not detect internet and just put you into the single-player campaign. I wrote a review on the game if you want to check it out (link below).