INDIANAPOLIS (WISH) — Legislation released Wednesday would add immigration checks and potentially remove thousands of households from the SNAP program.

Senate Republicans have released their top priority bill for this session. Designated Senate Bill 1, as is customary for the caucus’ priority bill each year, it would add tough new eligibility requirements for both the Supplemental Nutrition Assistance Program, or SNAP, formerly known as food stamps, and Medicaid.

The bill would prohibit anyone other than a U....