BEDFORD, Pa. — Art Halvorson makes for an unlikely Republican primary challenger to a six-term incumbent like Representative Bill Shuster. He is a newcomer to this quiet corner of south-central Pennsylvania who retired here after a long Coast Guard career.

But in the throw-out-the-bums anger percolating in the election cycle now underway, Mr. Halvorson, 58, believes he might have a shot to displace a name that has occupied this House seat since Mr. Shuster’s father won it in 1972. After two House elections dominated by the small-government philosophy of the Tea Party, 2014 may be driven by a less ideological but more emotional sentiment: clean house.

“People don’t remember a time before the Shusters,” Mr. Halvorson said. “They created an aristocracy, and people are so accustomed to that’s the way politics is done around here, they don’t see how he can be toppled. I’ve got to show leadership’s what’s important, not seniority, and longevity is not leadership.”

The outcome of this and at least 17 other primaries next year may have a negligible impact on Republican control of the House. Few would suggest that Pennsylvania’s Ninth Congressional District is in danger of slipping into Democratic hands. But in the heated battle over the ideological future of the Republican Party, races like this one could alter the complexion of the Republican caucus in the House — and Washington’s ability to govern in President Obama’s final years in office.