You should be able to make it thru TSA, don't know about getting onto plane and into Cabo.
Would bring cc of passport (if available).
From my trips to Mex. (making a Tijuana booze run by walking across the border then walking back) there was no checking of documents to enter Mexico - there likely will be checking to enter Mexico by air).
TSA should let you by, and allow your return to US, but you may not be allowed on the plane w/out a US passport.
TSA link:
http://www.tsa.gov/traveler-information/acceptable-ids
You might just go to the airport and see if you can get on - try not to check bags. Also improves chances of getting reticketed on a later flight if you present yourself at the airport v. saying you lost something and couldn't make it to the airport.
Hope something works