How to recover from a broken sudo

You cannot fix a broken sudoers file while logged in. You would need access to sudo for that...and it's broken. You can't get to the root account because it's locked in normal use.

So you need to reboot into a condition where root is unlocked and available.

1) Save all your work and then reboot.

2) Hold down the left SHIFT button to get to the GRUB prompt.
If you get a pretty splash screen, reboot and hold down the button earlier.

3) At the Grub prompt, select Advanced Options

4) At the Advanced Options prompt, select any Recovery Console

5) Watch the boot technobabble run across your screen.

6) At the Recovery Console prompt, select Drop To A Root Shell

7) You should see a warning about a read-only filesystem.
The prompt should look like '#'

8) Remount the root filesystem as read-write instead of read-only. We want to make changes that stick.

# mount -o remount /

9) Try a test write. It should not cause an error:

# date > /tmp/test

10) Okay, now go into visudo and fix your mistake.

11) When complete, reboot into normal Ubuntu.

# shutdown -r now