The airlines didn't go out of business the last time there was a severe pilot shortage, they just started paying for pilots' training costs.
I think you'll see the same thing this time. Only difference will be that instead of a major airline taking a guy from zero hours to a commercial certificate and putting him in the FE seat of a 727, he will go to the right seat of a regional jet. Plus, I can imagine some pretty wicked training contracts.
I don't think the glory of being an airline pilot is completely gone, I just think the risk/reward curve is screwed up. If you took a lot of the financial risk out of the career path, I think you'd find there was no longer a shortage.
Then there's always Plan B: There is (rough guess) probably close to 10,000 regional pilots at all the regional airlines. That's quite a large pilot pool for the majors to choose from, and it will eliminate the pesky regional airline thing at the same time.