HANCOCK, N.H.—Former Utah Gov. Jon Huntsman Jr. approached his first retail-politicking trip to New Hampshire with a caution honed by diplomatic training, as he declined to commit to positions on issues from Afghanistan to climate change.

But the crowds that packed a steakhouse in Hanover, a stately home on Keene's Main Street, a farmhouse in Hancock and a VFW post in Concord showed the open nature of the Republican primary contest here—and the potential of a candidate running to the center in a field crowded to the right.

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