Big number of connections

Hello!

We are going to build system based on PostgreSQL database for huge
number of individual users (few thousands). Each user will have his own
account, for authorization we will use Kerberos (MIT or Windows).
Most of users will have low activity, but for various reasons,
connection should be open all the time.
I'd like to know what potential problems and limitations we can expect
with such deployment.
During preliminary testing we have found that for each connection we
need ~1MB RAM. Is there any way to decrease this ? Is there any risk,
that such number of users will degrade performance ?
I'll be happy to hear any remarks and suggestions related to design,
administration and handling of such installation.

best regards
Jarek