Other word for an empty promise (that is likely not to be held)

I would describe such a reply as perfunctory:

1. performed merely as a routine duty; hasty and superficial: perfunctory courtesy.
2. lacking interest, care, or enthusiasm; indifferent or apathetic

I call it a lie.

Smarmy is a possibility; it means "Falsely earnest, smug, or ingratiating." Also weaselly, in sense "A devious or sneaky person or animal", may apply. An uncommon word that might be relevant is fugacious, "Fleeting, fading quickly, transient", if you expect support to just forget the issue immediately.

More along the line of "empty promise" are words as found in a clique of illusory synonyms: chimerical, fancied, fanciful, fantastic, fictitious, illusory, imaginary, unreal, and similarly for fictive and perhaps for tenuous, "thin in substance or consistency".

Empty promises in the sense of "say what they want to hear" often are called blandishments, which is defined as "flattering speech or actions designed to persuade or influence."

Empty promises may also be evasions, lies, sophistry. Among the senses of the latter are "an argument that seems plausible, but is fallacious or misleading, especially one devised deliberately to be so"; "the art of using deceptive speech or writing"; and "cunning or trickery".

A generic reply of this sort is what's known as a pro forma statement:

pro forma, adj. : Done as a formality; perfunctory. [AHED]