what is the verb for giving false promises one is unlikely to fulfill?

While saying something that isn't true is to lie, in your case you are asking for something more specific.

Deceive:

transitive verb

4 : to cause to accept as true or valid what is false or invalid · deceiving customers about the condition of the cars · bluffing at poker in order to deceive the other players

intransitive verb

: to make someone believe something that is not true : to practice deceit; also : to give a false impression · appearances can deceive

Her parents punished her for trying to deceive them.
He was accused of deceiving the customer about the condition of the car.

Here, the lie is part of a greater deception so that you can get something you want.

Empty promise

https://idioms.thefreedictionary.com/empty+promise

"A promise that is devoid of worth or meaning, one that cannot or was never intended to be carried out. John may be a sweet-talker, but in reality, he's a lowlife full of empty promises."

I would proffer the terms "prevarication" or more simply put, "to con", "conning"

In the act of "conning" his mark the grifter uses prevarication to convince his mark the forthcoming reward exists.