Except one country.
Guess which one...
The Holy See's response on the GA floor, meanwhile, was telling. While commending the declaration's call for the end to violence against homosexuals and the criminalization of homosexuality, the Holy See was concerned that the statement
"gives rise to uncertainty in the law and challenges existing human norms."
In other words, that it might actually make homosexuality acceptable, and the Holy See could never abide that.
The US position, like the Holy See's, is then somewhat problematic: they don't want to condone hate crimes or violence against the LGBT community, but they don't want to bestow legitimacy on it as a lifestyle either.
Still, it's very revealing that the sponsors simply read out an oral statement and listed the cosponsors. At this moment, it's impossible to imagine such a resolution passing on the General Assembly floor. (Though it is possible to imagine an extremely ugly debate over one.) Maybe a few years down the line that might change, but given the attitudes of many African and Asian countries on this issue, I doubt it will be soon.