It should take away from his support among self-identified Catholics, but on this policy it seems quite close:
A majority of U.S. Catholics support President Obama’s decision to require religious institutions to include birth control in health insurance plans, according to two new polls. A poll by the Public Religion Research Institute found that support among Catholics at 58 percent, slightly higher than that of the overall public overall at 55 percent. - http://www.drudge.com/news/153629/most-catholics-back-obama-birth-control
I figured they had some type of polling that if they could make the issue about "contraception" they wouldn't lose any real support. We both know it's really about govt control over religious institutions.