Megan, this is a tough one. It's the type of song most instructors would likely ask you to pick another one. However, from the standpoint of the words and the message, it is great song. I like Dave Matthews quite a bit, and if forced to do so, I would probably try to come up with some form of an almost freestyle looking dance with maybe some rumba overtones to it in hopes of keeping the romantic feel you are hoping for.
The song changes tempo and its stoccato more than a few times, so it would almost be like a show routine you'd see on Dancing with the Stars or something. In other words, to do the slow parts to a song like this is really difficult and you have to be very, very good dancers. It's also pretty long -- more than four minutes. That's usually not a good idea for a first dance at a wedding, but the DJ can fade it out at a predetermined point. When the song speeds up in its refrain, a traveling rumba step or Open Cuban Walk with turns might work.
Maybe someone else will come up with a far better idea, but in general, this is a difficult one for a true ballroom look.
