From the NYTimes articel posted:
"Many Democrats argued that the measure could actually harm immigrants who are victims of domestic crimes. There is no exception for people who fight back in self-defense against their abusers, or have been accused by their abusers of violence themselves, as there is in current statute. Several domestic violence victims advocacy groups have also opposed the legislation on those grounds."
That combined with the fact that there is already a very similar law on the books (with a narrower definition of domestic violence) suggests the issue is one of definitions.
That makes a whole lot more sense than every single Dem blah, blah, blah Outrage. blah, blah, blah.
And by the way, every single Dem did not vote against the measure. 61 voted for. But Outrage is more fun than facts.