MT. LEBANON, Pa.—For Republicans, it’s all hands on deck to help Rick Saccone win a special election for a U.S. House seat that is deep in Trump country.

GOP-affiliated groups—including the National Republican Congressional Committee, the House GOP’s campaign arm; the Congressional Leadership Fund, a super PAC aligned with House Speaker Paul Ryan; the Republican National Committee; and two pro-Trump PACs, 45Committee and America First Action—have poured about $9.1 million into the Pittsburgh-area race, according to a Wall...