You're assuming that the 40% that would vote against it wouldn't accept it. That is, just because they don't really like the idea doesn't mean they would be opposed to it.
There are people who really wouldn't care, provided a) the government leaves them alone for the most part, and b) they have access to justice (or at least no blocking of it).
You are quite right. Those who refuse to accept it at all, perhaps with violent opposition, would be a subset of those who voted against it.
But the question still exists. It is very difficult for a government based on the consent of the people to have legitimacy if a large minority of the people disapprove.
Or at least more so than for governments basing their legitimacy on some other principle.