Huh, what? You're talking about the first bill Obama signed into law? The GOP is reliably management-vs-labor, to be sure (after all, organized labor is a key element of the Dem constituency, so at least the parties are representing their constituents by their sides there), but how did they kill it?
I did think you were trying to construe the "people can pay for their own birth control" as a women's rights issue, since that's recently in the news - OK, I guessed wrong. So what are you on about?
(BTW, I do wish there was a party I was aligned with, but I just want a small government party, and there's no such animal any more).