promise the moon/earth/world
promise the moon (to someone)and promise someone the moon
to make extravagant promises to someone. Bill will promise you the moon, but he won't live up to his promises. My boss promised the moon, but never gave me a raise.
promise the earth
If someone promises the earth, they promise to give people things that they cannot in fact possibly give them. `Politicians have lost credibility,' he complained, `they promise the earth and don't deliver.'
promise the moon
If someone promises the moon, they promise to do or give things that they cannot in fact give. Politicians promise the moon at election time, but do they deliver once they're elected?