Unbeknownst to those who read only the Times‘ main story, the poll asked the same question to men. They were not split. Men favored opting out by a 20 point margin (57 vs. 37), except when a “religiously affiliated employer” was involved, in which case the margin increased to 25 points. Combining men and women, a substantial majority (51-40) favors allowing an opt-out–increasing to 57-36 where religiously-affiliated institutions are involved.

These are not close results. It’s hard to read this poll and not conclude that, contrary to some accounts, Obama wasn’t such a genius to pick a fight over mandated contraception coverage–because he appears to be losing the public debate on the question. That’s a conclusion the Times story effectively hides from readers.

It’s also one possible explanation for Obama’s otherwise somewhat mystifying overall drop in approval during the period–March 7-11–when the poll was in the field. But not an approved explanation.