You do NOT need TSA compliant locks, and it's probably not something I would recommend. Depending on how you interpret the law, TSA compliant locks are not compliant for flying with firearms, though the TSA says otherwise.
(Edited to say that you NEED locks, but they don't need to be TSA compliant is what I was trying to say)
Deviant Ollam has a good writeup series on flying with firearms. He has written for The Firearm Blog about it and has a video series about it. He actually uses firearms so that he can secure the rest of his belongings with a non TSA compliant lock.
If you can't afford the Pelican case, you can go for one of Plano's AllWeather offerings. They're not as tough (no reinforcements around the lock holes for example), but they're better than your average gun case. I've been packing mine (only a 36") for a flight this weekend. It's not the best packing job, given that I plucked the foam for an MP5 instead of a shotgun, but I think it will do...