If anybody responds, tell them that the offer is oversubscribed and that it is no longer available.

I wonder what is wrong with saying just "Hi, I would like to get feedback about project X.". Would that way have the same affect?

I'm asking that just becasue I try to follow an old proverb (not sure if translation to English is correct): if you have a smallest doubt about whether to lie or not, don't lie.

(no, I'm not good with the above rule, but at least helped me while dating and now in marriage)