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.
Yes, you have chosen a long, tough song. But I have to disagree partly with DHeun: it never changes tempo, only mood. You can do a Nightclub Two-Step or Society tempo foxtrot or combination of both to this, with more lively movement, spins and turns during the "Crazy/Crush" refrain. I would stop at 2'04", or 2'26 if you want to do the refrain twice.
This will take some practice and some dancing ability. It is not a beginner's dancing tune. Find a skilled and understanding instructor. If it's just too much, try this:
1) Learn a simple rumba box step and get the rhythm down so your feet can do it in your sleep.
2) Now forget the box step and just do the rhythm with your feet, with your fiance, keeping a good-looking frame as you move around any way the music takes you. Use this for all the sweet romantic slow parts.
3) Do a 70s-80s style freestyle during the louder/busier "refrain" parts.
No, it does change tempo, not often and you have to actually count the whole song to catch it happening, but the problem with that is that it is going to make you look like you're stuttering when it happens.
Pay someone to choreograph it if you want it to look good. If you just want to dance and you don't care if you look good then do the rumba box thing and you'll get through it.
A Nightclub 2-Step/ West Coast Swing combo is my feel on this one. Both have a smooth, sexiness to them, like the song, but they leave a lot of room for groovy interpretation for the jazzier bits.
If you are beginner dancers you'll pick up Nightclub 2-Step really fast. Then have your choreographer work in some WCS, which is little more challenging.
Great song, but remember the most important part of the wedding dance is that you two are expressing your connection through music. Be cautious about over-choreographing to complex song to the point that your movement is foreign to you and you look like strangers to each other. Even basic steps done well will make your guests get misty-eyed.
When's the wedding and have you partner danced together before?
I agree that the music is way too long. Think about having it reduced to under 3 minutes at a sound studio. The next step is to structure the peak and lift, with a few twirls leading up to that. And, yes, you'll need good shoes and time rehearsing.
Wow, super difficult song. However there are some good suggestions from other posters. I will caution you not to expect twirls and spins. First, they are harder than they look. New dancers have a hard time mastering them without falling over. Second, will you be able to turn in your dress and shoes? Most brides pick very high heeled shoes that they are not use to and are totally wrong for dancing. Do not confuse dance shoes with street shoes. Dance shoes are constructed completely different with suede soles. Chances are your dress will be too long. Keep your wedding dance length under 2 minutes. Ideally, a minute and a half is enough. You'll be amazed how long that seems when you are dancing. Also, any longer and your guests will get bored. Have the DJ fade the song out at a good spot in the music. Get a simple choreographed routine and keep your heads up. We had one couple at our studio where the woman kept her shoulders up by her ears and her elbows and head down. She looked like a vulture. No amount of instruction could fix her. Her video must have been cringe-worthy.
This song doesn't fit a typical ballroom music. If your priority is the music, then you'd have to find a dance to sort of fit the music. If your priority is the dance, then pick a dance style first and find a music to fit, which would be alot easier.
If you can dance on the beat, and can dance a basic step or two of some known style, you're already better than 99% of the wedding couples.