Encrypted cookies

Somebody here is developing a Web application that requires user logins, 
but that is unable to store session information on the server (don't ask 
me why, it's a long story). So here's what they propose: to take the 
username, hash of the password, and date the user logged in, encrypt 
them with a strong encryption algorithm, and store them in a cookie 
(along with a hash to ensure integrity).

My question is, assuming a proper encryption algorithm/eky are chosen, 
can anybody think of a problem that this will create that sessions don't 
already have (namely, replay attacks)?

I've thought about this for over a day, and I can't think of any obvious 
problems, but I could be missing something.

Thanks!

Ron

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