No, but equity before the law is.
Yes, but it takes an overwhemling majority. At least it does in Canada, I can't speak for the US. Here any change requires approval minimum of 7 of 10 provinces which must combine for a minimum of 50% of the population. Since our Constitution was implemented in 1982 there have been no changes. There was a referendum in the early 90s on a number of changes but it failed.
There is also a notwithsatnding claus ethat Parliament can use to override it, but this clause is meant for emergency use, and any government which uses it would pay a very large political penalty for doing so.
As well, even many opponents of gay marriage would probably balk at the idea of removing an equity before the law clause, that could come back to haunt just about anybody.