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Catholic voters give Obama a 46-39 percent over Romney, although those percentages are nearly flipped when that is restricted to white Catholics, with the former Massachusetts governor holding a 48-37 percent lead. The numbers are a testament to the president's popularity among Latino voters, who are predominantly Catholic.

Obama also holds leads among white mainline Protestants, leading Romney 50-37 percent. And the president shows strength among religiously unaffiliated voters, leading Romney 57-22 percent.

The poll showed that a majority of voters — 58 percent — said that it was either not too important or not at all important for a presidential candidate to share their religious beliefs.

That number could be down significantly because neither candidate seems to have connected with the electorate on religious grounds. Only 38 percent say Obama's religious beliefs are similar to their own, versus a mere 30 percent for Romney. Around half of voters correctly identify Romney's faith as Mormon.

The president's decision Wednesday to publicly express support for gay marriage might have been partially influenced by an acknowledgment of his standing in the polls among evangelicals. Already trailing dramatically within the group — among the most vocal opponents of same-sex marriage — the president's campaign team might have decided there was a reduced risk in endorsing gay marriage.

But on Wednesday, Obama said the politics of the announcement were not yet clear.

"I think it'd be hard to argue somehow this is something I'd be doing for political advantage, because, frankly, the politics — it's not clear how they cut. But I'm not going to be spending most of my time talking about this because frankly, my job as president right now, my biggest priority, is growing the economy and making sure we put people back to work," Obama told ABC News.