WAUTOMA, Wis.—Brian Gerrits, who oversees two dairies that own more than 5,000 cows, is one of Wisconsin's many dairy farmers backing the immigration overhaul heading to the U.S. House.

Giving illegal immigrants the chance to become citizens would eliminate anxiety for farmers and workers and "take that monkey off our backs, and theirs," Mr. Gerrits said, while taking a break from mixing pancake batter at a Waushara County dairy breakfast attended by U.S. Rep. Tom Petri (R., Wis.).

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