When Shelly says 'luggage tags from the airport' she means the claim receipts you get when you check your bags. They usually staple them to your boarding pass envelope.
DME tells us that they need 10 days to print up your packet and get it to you. You 'should' be okay. It's the holidays, so that may have some effect on your packet. If you don't get the packet, don't worry. You can show those claim receipts to the DME CM (at the counter) and they will have someone go to baggage claim and get them for you. They will also print up vouchers for your bus ride at the counter as well.
I would be very tempted to just get the bags myself if the tags don't get there in time. I hate the thought of my bags being unattended for any amount of time. And that is what will happen if they have to send someone to get them. Who knows how long it will take to get someone there, to baggage claim. Your bags may be unattended for quite awhile!!