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Mrs. Bachmann, popular with Iowa religious and social conservatives, is expected to do well in the poll, though she doesn’t have as large a campaign organization in place as former Minnesota Gov. Tim Pawlenty.

But privately, senior Republicans in the state say the candidate to watch is Mr. Perry, who on Saturday held a national call to prayer, an event at the Reliant Stadium in Houston attended by an estimated 30,000 people.

Perry supporters said that any announcement would have to come after the prayer day event lest it be interpreted as a political rally.