Speaking internationally, the worst case scenario for Sony is this: They have a system built for Japan (i.e. the Japanese like "hardcore," dedicated gaming portables) but software built for the US (ports of PS3/360 games like CoD), and it tanks in both places because the Japanese don't want the software and the dudebros don't want the hardware (dudebros are literally the last demographic I see being willing to give up their big screen TVs).
Best case scenario: Japanese software picks up, and the PSV does what the PSP did in Japan; the US software library becomes highly varied -- not just the number of titles, but also the type of titles, encompassing Android games like Angry birds in the free-5 dollar range, PSN titles in the 5-15 dollar range, cheap-o PSV titles in the 20-30 range, and "big blockbuster" titles in the 35-50 dollar range. This enormous variability manages to attract gamers from a wide variety of interests even if it doesn't dominate and control any of those ecosystems independently.
All of this is vague hand waving, though. I am very much a "let's wait and see what happens" type of person. Consider the phases/cycles of doom and then victory and then despair we've already had:
1) When 3DS was announced, its initial third party support seemed so overwhelming that everyone thought it was a sure fire hit.
2) By the time it launched, due to pricing and battery concerns along with several third party misfires, this opinion had completely changed, and suddenly the 3DS seemed doomed.
3) Vita was announced. With the 3DS weakening, Vita's chances seemed quite good.
4) 3DS price cut and game announcements. Suddenly the 3DS was no longer doomed.
5) Vita launches. Now Vita is doomed.
We've gone back and forth so many times, now, and this is before including any discussion about iOS or Android. But I want to point out that this sort of volatility of opinion should be expected, because the handheld gaming industry is undergoing enormous change and it's especially difficult to see in to the future when fortunes are changing so rapidly. And for precisely that same reason, I don't think it's prudent to be alarmist in regards to the PSV's long term successes.
I feel comfortable saying the next 4-6 months are going to be rough for the system. Beyond that, I'll wait and see. For now, again, all I feel I can offer is vague hand waving.