The sudo command checks the permission of the /etc/sudoers file and also the contents of /etc/sudoers.d/ before allowing you to use the sudo command.
For example you might be warned:
sudo: /etc/sudoers is mode 0777, but should be 0440
or perhaps:
sudo: can't open /etc/sudoers: permission denied. sudo: no valid sudoers sources foundm quitting
Therefore, if you don’t have root login (which is generally good security practise) then you might not be able to change the permission back without dropping into recovery mode.
1 – Reboot the machine
2 – Select boot from recovery more
3 – fsck the disk which will then mount the disks as read/write
4 – Drop to root shell
5 – chmod 0400 /etc/sudoers
6 – reboot the machine and you are fixed