Ok state referendum passed with flying colors in 1861. So apparently then the “people” were convinced.
I think you will need a broader consensus than just a referendum in one state. However, I believe that if you could demonstrate that a large majority of residents in a state favored separation, you could induce the American people to try to find a way to accommodate them. Scotland talked London into permitting the people of Scotland to decide that kind of issue. I think it could be done.
But, we're not going to find out any time soon because the vast majority of people in every state value their American citizenship and want to keep it. In the 1860's, there were some people who thought that staying with the Union might lead to the loss of what then many have been the most valuable asset class in the world (slaves).
That's not true now. No one agrees with everything and not everyone is succeeding in our economic system, but a lot of these folks wouldn't do well in any economic system. Enough people are succeeding here that I wouldn't be counting on any mass movement in favor of separation.