I don't think we assume the phone to be compromised here, so storing a very long key on the phone in advance and then using it piece by piece is not problematic, if we're only concerned about end-to-end security (i.e. that no malicious base station or similar can read the messages).

If we assume that the attacker also controls the phone anyway, then he can just see the message directly.

To be clear, the idea is still extremely impractical, but password entry should not be the problem.