TUCSON, Ariz.—Andy Goss knows exactly what he'll do if he wins his long-shot race for Congress. First, he'll cut lawmakers' pay 40% to $104,400. Then the former Army interrogator will use the savings to build a Capitol Hill barracks where all 535 senators and representatives will be required to live.

"If our military has to live in such a fashion, I think we congressmen should also," says Mr. Goss, one of four men seeking the Republican nomination in southeastern Arizona.

This...