Directly? Yes. They can, of course, vote with their feet or elect representatives that could attempt to reconcile. The historical record, though, doesn't seem to support giving the people a direct choice.
This really isn't all that concerning to me, really. This is what representatives do; they represent. Yes, it's a big decision, but just because it's a big decision doesn't mean that we need a referendum.
If memory serves something like 8 or 9 out of the 11 rebelling Southern states gave their population a choice - either through referendum or electing delegates to a secession convention. I'd say that the historical record lies the other way. If people are going to be given a choice between losing their homes and losing their citizenship then I suggest they deserve a say in the matter.
This is what representatives do; they represent.
Shouldn't they represent what the people want? What if only about 45% want to leave and the legislature takes them out anyway. That's a satisfactory solution for you?