I edited /etc/group to add myself to another group, raising my total to 33, and I was no longer able to log in. /var/log/secure reported "fatal: getgroups: Invalid argument". Some googling revealed the source of the problem, that getgroups returns EINVAL when the number of groups exceeds a kernel limit (NGROUPS_MAX in /usr/include/linux/limits.h). I'm not sure what the best fix is, but one shouldn't be locked out of logging in when another group is added to one's list. sshd should fail in a more graceful way, for example allowing the login but without all supplmentary groups available, and a warning issued to the login terminal and the syslog. See also bug 145492.
It seems to be working fine in FC3.