You *will* need to provide a credit card or something to that effect for each of you that is travelling for identification purposes if you use a check-in desk without bringing your comfirmation with you.
The alternative would be to bring a copy of your booking confirmation which should have a barcode printed in one corner and your booking reference in the other. You can scan this at the self service check in machine and it should check you both in no questions asked. Or bring your booking reference which you can also type into the main screen.
Basically you have a good chance, try not to highlight the fact that the names are wrong initially to anyone as it is only a domestic flight. In a worst case scenario you would have to buy a new ticket for the Mrs, but I think if you stick to the above advice you should be fine.
Or as Crowe said...just check in online, there would be no problem at all as no further ID would be compared to the online boarding pass you print at home. Oh...and Helo...one more thing.....don't do it again naughty!!
Agent X