Maybe 10 years ago, sure it could have happened.
Now that we will soon have 4 major airlines (UNICAL, DeltaNW, USairAA, and Southwestran) I just can't see it happening. The levels of pressure that would be brought to bear on both management and the union would simply be unimaginable. It has been well established that the public has no sympathy for "already overpaid" pilots, and management would not fair any better.
FedEX and UPS are in the same boat. If a strike shut down Memphis for more than a week, I could see the postal service taking over and the USAF doing the flying.