I think that if a large majority of residents in a state really wanted to secede, we probably would try to find some way to do it legally. However, I'm not sure what steps that might involve.
Like you say, though, there are no such states. I suspect that most of the very few people who dream of secession live in states that, as I pointed out in post 690, have become most dependent financially upon the government of the United States of America. (I want you to picture some drunk on the sidewalk outside of the Department of Public Welfare screaming, "If you don't return my phone calls, I'm going to quit cashing my welfare checks!!") That's not likely, is it?
However, if a large majority of the people of a state genuinely wanted to leave, we would probably need to at least try to develop some new procedures to accommodate them. It would be a very tricky matter. The notion that the USA is just some sort of revocable joint venture of the states and that any state can leave at will was, of course, utterly repudiated. The United States involves a bond between the people of the United States ("We the People") and those bonds between the American people cannot be severed by any state. We are citizens of the United States of America and our state government cannot just cancel our U.S. citizenship. That was the mistake of the seceding states in the 1860's. Similarly, as things now stand, the United States government cannot just sell the state of Mississippi to the Chinese. The People in the affected states have rights.
We're all in this together and, fortunately, all but a few of us are very happy to be Americans. It'll all work out.
It was repudiated by force, but has yet to be repudiated by reason. The Founders said explicitly that people have a right to independence, but some times the King wins a clash of arms and denies them their right.