What was the GOP's goal with playing with the VAWA? It doesn't take a damn political strategist to see that it's bad politics, especially when your party is hurting so badly with women, and an election just ended showing that. All they achieved was giving Dems more ammo against them with women voters and keeps the war against women campaign as an albatross around their necks.
This is the whole problem the GOP is facing right now, though -- the House is the only place where Republicans are powerful (hence visible) and the Republican House is straightforwardly bad at politics because national politics is not a key skillset for representatives. Opposing stuff they really have to pass because they're angry about it and their local districts are way to the right of the country and then getting steamrolled into voting for it anyway is like the entire House Republican deal right now. And the best part is, every time it happens they get even more angry and swear that next time they won't do it. That's why Boehner basically completely gave up on talking about the sequester until it happens.