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“I’m not going to sacrifice my integrity for anyone or any party,” Mr. Jones said. “It’s the price you pay. I didn’t come up here to be a puppet for anyone.”

Few options are available for rank-and-file lawmakers to get back at leaders, but one would be to withhold their vote for Mr. Boehner as speaker when Congress votes Jan. 3.

Asked if he’d go that far, Mr. Huelskamp quipped, “You know, the Fiesta Bowl with [Kansas] State’s the same day.”