It's not even close: By a lopsided margin of 66 percent to 26 percent, Americans support President Barack Obama's proposal to require private health insurance plans to cover the full cost of birth control for women, according to a new CBS/New York Times public opinion poll.

Rephrasing the question to ask specifically about "religiously affiliated employers, such as a hospital or university," barely moved the needle, to 61 percent to 31 percent.

Those numbers, which come with a margin of error of plus or minus 3 percentage points, are better for Obama than his numbers on foreign policy (50 percent approve, 36 percent disapprove), Afghanistan in particular (51 percent approve, 36 percent disapprove) and are nearly the mirror image of public opinion on his handling of the federal budget deficit, where he loses 32 percent to 59 percent.

National polls can understate the political danger of a given issue. Congressional Democrats fretted last week that the firestorm could cost them dearly among blue-collar voters, especially Catholics., in states like Pennsylvania. Some Democrats complained privately that the

"culture war" clash drowned out the positive news about the economy.

The poll was conducted from Feb. 8 to Feb. 13. It's not clear what impact Obama's proposed "accommodation" to religious institutions will have politically.

Olivier Knox is the White House correspondent for Yahoo News.

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