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“We’ve said that’s not fair game,” he said.

Both sides now have promised that religion will be off-limits in the campaign, but Republican National Committee Chairman Reince Priebus thinks that the Obama team actually would be happy to have Mr. Wright or Mr. Romney’s faith take center stage. Mr. Priebus said the administration is looking for a distraction from the struggling economy.

“He wants this story to play out in the media. He can’t change the truth and escape the reality of where we are in this American economy,” Mr. Priebus said, also speaking on “State of the Union.”

On ABC’s “This Week,” House Speaker John A. Boehner, Ohio Republican, echoed those sentiments and said it will come down to Mr. Obama’s economic record and Mr. Romney’s plan for the future. He called the plan to attack Mr. Wright “nonsense.”

On the same program, Mr. Boehner’s Democratic counterpart, Minority Leader Rep. Nancy Pelosi, California Democrat, agreed and flatly said, “This election is not about Rev. Wright.”