In older OS X versions, this used to work just fine:
defaults write /Library/Preferences/.GlobalPreferences com.apple.mouse.tapBehavior -int 1
It would enable tap to click for built-in MacBook Trackpads for the root user, which would also affect the login screen. There are similar commands to enable it for Bluetooth-based Magic Trackpads as well.
Unfortunately it doesn’t seem to work in OS X 10.8 anymore. Is there some other way of doing this in Mountain Lion?