Sarah Posner nicely summed up the conventional wisdom on a particular red-hot subject yesterday:

First there was Michael Sean Winters, writing “J’Accuse!” in the National Catholic Reporter. “President Barack Obama,” Winters wrote, “lost my vote yesterday when he declined to expand the exceedingly narrow conscience exemptions proposed by the Department of Health and Human Services. The issue of conscience protections is so foundational, I do not see how I ever could, in good conscience, vote for this man again.”

Next up was E.J. Dionne, a good liberal Democrat (and Catholic), who used his Washington Post column to assail the President for how he “utterly botched the admittedly difficult question of how contraceptive services should be treated under the new health-care law.”

Mark Shields, also Catholic, opined on the PBS NewsHour: “The fallout is cataclysmic for the White House and for the president.”

Doug Kmiec, the former Reagan administration lawyer who backed Obama in 2008, now says he may not in 2012, over the contraception mandate, and that alone.

With all this Chicken Little talk flying around (at least, as Posner notes, among Catholic men), I looked with more than average interest today at two new polls testing the reactions of Americans, and particularly Catholics, on the issue. If the contraception mandate is going to turn the entire election against Obama, it is not apparent from the numbers.

Here’s the key finding from Public Policy Polling’s survey:

A solid 56 percent majority of voters support the decision to require health plans to cover prescription birth control with no additional out-of-pocket fees, while only 37 percent are opposed. It’s particularly noteworthy that pivotal independent voters support this benefit by a 55/36 margin; in fact, a majority of voters in every racial, age, and religious category that we track express support. In particular, a 53 percent majority of Catholic voters, who were oversampled as part of this poll, favor the benefit, including fully 62 percent of Catholics who identify themselves as independents.

The numbers barely budge when respondents are specifically asked about health coverage for employees at Catholic hospitals and universities, in a question framed to include the Bishops’ argument that their religious mission requires an exemption.

The Public Religion Research Institute also released a poll today that showed slightly weaker support for the mandate among Catholics if the question is framed as one of religious liberty, but not by a very big margin. According to PRRI, 58% of Catholics support a contraception mandate; the number drops to 52% if only registered voters are considered. When specifically asked about Catholic hospitals and universities, 52% of Catholics still support a mandate, and that number drops to 45% (with 52% opposed) among registered voters. PRRI did not provide crosstabs breaking out the numbers by partisan affiliation.

If you think these numbers look suspiciously like the general pro-Obama, anti-Obama breakdowns you see in every poll, you are thinking right. 2008 exit polls showed Obama winning Catholics by a 54-45 margin. It would be reasonable to assume that a sizable majority of the Catholics saying they have issues with the contraception mandate in the PPP and PRRI polls are inclined to vote against Obama in any event, particularly given the very noisy GOP effort to exploit the issue. And that’s certainly what the partisan breakdown in the PPP survey indicates.

Some might argue that the electoral impact of the dispute could intensify if Catholic leaders begin to threaten such dire consequences as a shutdown of hospitals and universities. Aside from the strong possibility that such threats might invite a pretty severe backlash from people who rely on these institutions–including the majority of Americans who believe the Bishops are simply wrong–there is the inconvenient fact that a number of states–including New York and California–already require contraception coverage in employee health plans with no exemption for religiously affiliated institutions. Why haven’t Catholic institutions in such states shut down already? When such data points begin to gain public attention, some of the screaming–such as Pittsburg Bishop David Zubik’s claim that “at no time in memory or history has there been such a governmental intrusion on freedom”–will begin to look a bit ridiculous. Another talking point you can expect to hear a lot is the common-sense observation that health insurance is a basic form of employee compensation, no different in nature than a wage. Certainly a sizable majority of women–Catholic and non-Catholic–of child-bearing age, and more than a few men, who work at Catholic hospitals and charities are willing to use their wages to purchase contraception. Somehow, that subsidy isn’t considered institutional suicide for the Catholic Church.

I suppose it’s possible the Bishops and their allies can so polarize the issue that Catholic voters could begin to feel the tug of loyalty, and side with their Church even though they disagree with it on the very topic in question. But it’s something of a stretch to believe large numbers of Catholics who are willing to defy the Bishops every day and commit a mortal sin–worthy of eternal damnation–by practicing contraception are going to let the same authorities instruct them how to vote in order to defend the very same “teaching.”

In any event, it appears the administration may be suing for peace by indicating a willingness to compromise on its policy. I don’t know what kind of compromise would succeed in placating the Bishops, who are clearly using the contraception fight as part of a broader effort to pretend their religious liberties are in danger.

But if the administration decides not to back down, there is little empirical evidence at present that it is thereby courting electoral disaster.

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Ed Kilgore is a political columnist for New York and managing editor at the Democratic Strategist website. He was a contributing writer at the Washington Monthly from January 2012 until November 2015, and was the principal contributor to the Political Animal blog.