To be honest, when people started mentioning the Dempsey to Spurs rumors earlier today I was ambivalent. He has never been my favorite player and seems like a bit of a prick.
To me, ever since Klinsmann's took over the USMNT Dempsey seems to have changed. He seems more ambitious, he's hungry for the next challenge, and I don't think he handled his exit from Fulham well. My opinions on his exit from Fulham haven't changed just because he plays for my favorite club now.
From a footballing standpoint it makes sense though. He's essentially a van der Vaart replacement, he'll probably rotate in that central position in support of Adebayor along with Gylfi Sigurdsson, whom Liverpool also tried and failed to sign. Unlike van der Vaart, he can put in a 90-minute shift. Unlike van der Vaart, he can play on the wing if called upon. Without Dempsey, cover for Bale and Lennon would be down to Andros Townsend and David Bentley.