I'm struggling to think of a word to use for the title phrases. The context would be someone promising to do something and it being met with the answer "yeah right" or "yeah I've heard it all before" So I want to finish the sentence - This was initially met with ----
I confess your question is somewhat confusing to me. My answer below is targetted towards your last sentence, "This was initially met with ----."
This word has fallen out of use, but dubiosity fits the context.
Skepticism - a skeptical attitude; doubt as to the truth of something
"This was initially met with skepticism."
Depending on the exact exchange and the tone, the response could be considered dismissive
reacting to something in a way that shows you do not think it is worth paying attention to
An alternative in the same vein is derision
the opinion that someone or something is stupid, unimportant, or useless
If the tone was not so pointedly negative, it might be considered humoring. Humor (the verb) is defined as
to agree to someone’s wishes in order to help improve that person’s mood or to avoid upsetting him or her