Both sides tend to paint each other with pretty broad strokes, so lets not play pretend here shall we.
The general GOP stance on issues like birth control, abortion and "handouts" is that the GOP is quite firmly against all of those things. They dont want to fund places that do abortions. They agree with business being allowed to not only restrict what types of birth control their healthcare plans offer, but even more recently the Republicans in Missouri proposed legislation that would allow a company to fire a woman who even uses birth control. And in general, the GOP is against "handouts" or "entitlements" and wants to reduce the number of people being supported by those programs, without any solutions on what to do with those people once they are no longer supported.
If "some" Republicans dont support those measures, thats great - but it certainly puts you in the minority, and it also goes against the general GOP agenda that they are actively pushing through right now.