Can you explain how private messages would work in 184 characters? To me it seems counter intuitive to a public blockchain. Just curious. :)
Encrypted data isn't necessarily that big. The chances of your data being cracked is about equal to chances bitcoin signatures are cracked. Quantum computers in the future may though.
The NSA is keeping a record of everything sent over ISP channels. Someone at least potentially has these messages anyway. Anything sent over the internet has this problem.