I don't think the Orlando airport has limousines just 'hanging around' waiting for customers. As far as I know, you need to reserve one in advance, so you can't just decide on landing that you want to take a limo.
Who's making the travel arrangements? As suggested above, just tell your fiancee the luggage tags didn't come, or there was a mistake and Disney's not going to be able to get the new paperwork to you before your trip.
With luggage tags, your luggage WILL be pulled before any bags are placed on the carousel; if you then don't check in with DME and have your vouchers scanned as you board your bus, your luggage could very well never leave the airport.
On the other hand, if you DON'T attach the tags you have two options:
1) Register for DME; give them your claim checks (or the numbers) and a description of your bags. CMs will pull your luggage and get it onto the DME trucks.
2) Register for DME; go to the luggage carousel, pick up your own bags and take them to the counter and then the bus with you. If you supposedly choose this option, instead when you come down the escalator there should be a chauffeur holding a sign with your name on it. THAT'S when you tell her you're going to Disney in style.