Even a constitutional amendment would be of questionable means, because the Federal Government would have to agree to a release of some sort-it's similar to how a state amendment barring gay marriage/civil rights is largely ignored.
It's pretty sad to again see a rush towards independence, let by the usual suspects
The current constitution doesn't foresee independence, although it would be an action of folly for the Federal Government to prevent independence for a region that has voted for it.
In the case of the Northeast referendum, we would've opened negotiations with the Federal Government - to resolve certain issues - with the Northeast becoming independent two months after the referendum.