To promise someone the world, promise someone the Earth or promise someone the moon are all hyperbolic idiomatic statements which exaggerate someone's claims or overestimate what they can deliver. 

1. Politicians have a tendency to promise the earth when they're running for election, and then fail to deliver if they win.
2. The internet provider promised the moon over the phone when I purchased a subscription but now our Internet keeps dropping and our connection is terrible.

1. If you keep promising your clients the moon to get their business, soon no one will trust you.
2. My boss promised me the world to get me to sign a new contract, but it was all a pack of lies.