The "Everyone" group is a built in group for all registered users...
try addind the group "Anonymous" which is a built in group for
unregistered users. This group will not ask for a username and
password.

However, i believe windows will ask for a registered user first... you
might need to run 2 logical printers on the server each pointing the
the same physical print device, one for everyone, one for anonymouse
only with no other groups. At this point you can set the registered
users printer to a higher priority number giving those print jobs first
priority.

Additionally im not sure if this will work on Win NT.
Please post a follow up