I think there is a lot to worry about.
First, scabs. Yes, some will cross intially, then some later. Some will come from off the street. Looking at the current job market, there are still a lot of qualified pilots out there who would rather be flying jets than working at Home Depot. And looking at the conditions of the majors and the long-term prospects of the industry, I don't think too many people will be concerned with being called a scab. It's not like it will come up in the UAL interview anytime soon.
Second, Delta Air Lines. If they have too, they can drop ASA like a hot potato. They could, in theory, file Ch. 11 and use that to get rid of ASA. They would simply tell the courts it is part of their reorganization plan in an effort to streamline to be more efficient.
Delta could distribute the void in flying to other regionals, to include SkyWest and Comair. SkyWest could stand to get a lot of ASA's equipment and routes, and being non-union they could be a viable candidate. Also, look at the other regionals out there who are looking for work. The carriers operating under US Airways Express would also be good candidates. If Delta had to, they might be interested in code-sharing with Independence Air. As a last resort, Delta could add some parked aircraft of it's own to pick up some of these flights. And as even last-last resort, Delta could cut ASA, take the assets, and start up another carrier.
There is no shortage of carriers out there who could pick up ASA's flying, whether it be through a code-share or a long-term agreement.
Third, pilot shortage. Finding pilots would not be a hard job for Delta, especially with a lot of RJ qualified people on the streets already looking for work. Also, can you imagine how many people would cross a picket line at ASA if Delta were to go down to ERAU and recruit people right out of school for an FO position? They would stampede all over each other to get there. Personnel will be found.
Finally, I think a short-term strike COULD be beneficial. I say that only because it would get the airline's attention. Who wants negative publicity, especially after what happened last week with Comair and US Airways. A long-term strike could have negative consequences though. Personally, if that were to happen, it's likely Delta would cut it's losses and run, leaving ASA out to dry.