sudo chmod -R a+w * cause
sudo: /etc/sudoers is mode 0640, should be 0440 sudo: no valid sudoers sources found, quitting
and how might it be made to work?
I think your best bet is to start the system in recovery mode (see here for instructions), drop to root shell and do
chmod 0440 /etc/sudoers.
EDIT: as Mik suggested below, the following should work as well without rebooting the system:
pkexec chmod 0440 /etc/sudoers
Why might the command cuase this to happen? I suspect you ran the command while your current directory was
sudo refuses to work if the permissions of
/etc/sudoers have been tamprered with to avoid compromising the system. You will have to fix the permissions using recovery mode unless you have another way of getting root access.