Most people want something for nothing. This issue was very well played by Obama. He made the Catholic Church and other churches come out and oppose something most women and many men want.
Look at the stats. Well north of 90% of women on are birth control at some point of their life. That includes Catholic and muslim women in the US. The cost is nominal really, but everyone loves something for “free”. The Catholic church has not been very successful in fighting chemical contraception, or very active. This dust up has been a very big surprise to many women in and out of the Catholic church. They thought it was their RIGHT to have birth control, and someone else pay for it. Not to mention that when states like Illinois mandated a similar thing, there was not even a squeak out of the Bishops.
Obama managed to increase his share the female vote, and made the Church look stupid. Most people will not look any deeper than that. Sad really. Beloc was right, people do not really want freedom, they want security. This is a perfect example of it.
For the record, I don't want to pay for someones pills by the threat of force.
If we're at the point as a nation where we'll throw away our Constitutional rights for "free stuff" (and we very well may be), the republic is doomed. We're just rearranging the deck chairs on the Titanic at that point.
As far as the Church looking stupid, sorry, I don't see it. Our position is well known; if people thought that made us stupid, they thought that already.