As a former NH resident and frequent visitor, I've been following this story with interest. I seem to recall that the last time this got shot down, it was due to the relative ease of obtaining a permit (that is, not a substantial burden). I certainly didn't think $20 for four years was a big deal, especially considering I got my permit in five business days.
However, as a non-resident, I was irked to learn that our permits went up to $100. I let mine lapse, since I usually visit the northern part of the state and open carry is legal without a permit. My routine is to pull over at the first rest stop on Route 91 in VT, get my weapon out of the trunk, and carry on.
Anyway, constitutional carry would be useful for a non-resident so I support the measure. It would be nigh impossible to claim that the practice has caused any problems in Vermont.