Web check-in to Mexico and Canada was introduced here just a month or two ago (I forgot... after a week, it seems like ages ago). You'll definitely be able to do web check-in for a flight to Mexico up to 24 hours prior to departure. ... Also, you could check in that morning at any airport kiosk (throw a rock any direction at SEA-TAC, I swear you'll hit one) or an agent could check you in, if you want to wait in line.

As far as the bags go, you can only check bags a maximum of 4 hours before departure time, so you won't be able to do that in the morning. Also, I know that agents have been told not to interline bags via Mexico, but I'm not sure if that's just for the resort destinations or if that includes Mexico City. Just an FYI, you may have to reclaim your bag at MEX and check them in again with MX to CUN. It had something to do with interline transfers not working properly in Mexico (again, it might just have been the resort destinations - seems very odd that it would be a problem in Mexico City).

Have a great trip!