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Recent polls show that Mr. Christie is leading the likely presidential primary field in New Hampshire.

Asked whether the RGA planned on putting money into Mr. Havenstein’s campaign, Jon Thompson, a spokesman for the group, dodged the question.

“There’s no doubt New Hampshire Democrats are panicked about Maggie Hassan’s re-election hopes,” Mr. Thompson said. “Lagging behind their neighbors in economic development, Granite State residents are hungry for new leadership to drive New Hampshire’s comeback. Walt Havenstein is a top candidate with 30 years of private-sector business experience who would be ready to govern and lead right away.”