promise someone the moon
US /ˈprɑmɪs ˈsʌmˌwʌn ðə mun/
UK /ˈprɑmɪs ˈsʌmˌwʌn ðə mun/

1.
to make extravagant or impossible promises to someone
:
•
He's always trying to promise someone the moon to get what he wants, but he never delivers.
•
Don't believe him, he's just trying to promise you the moon to get your vote.