Absolutely stupid, stupid, stupid idea.
Clearly, if the Dems were so desperate as to play "The Mormon card," their campaign would have been beyond redemption by that point, and the desperate Dems would be seen for what they would be, religious bigots of the worst sort, and Obama as the biggest religious bigot of them all.
Obama would as well be seen as a liar, and for god reason , as he said early in the campaign, that Romney's faith would not be a campaign issue.
By the way, it was not only the Mormon Church that supported Proposition 8, but also the Roman Catholic Church, Knights of Columbus, Union of Orthodox Jewish Congregations of America, and I believe as well some Muslim groups.
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First time ever I ever said this, but I agree completely with Winfield. This would be a mistake of the highest magnitude. Of course, the Obama campaign is highly unlikely to make such an error of judgment so I am not concerned about it happening.