Gov. Rick Perry is finding himself on unfamiliar battleground in the Republican nominating contest — attacked hard from the right — as the immigration and education policies he has supported to cultivate Hispanic voters put him directly at odds with the GOP’s conservative base. Perry opposes several immigration measures that Republicans like, including a U.S.-Mexico border fence and an Arizona-style legislation to require that police ask those they stop about immigration status. But the thing that continues to dog him on the campaign trail is the 2001 law he signed that allows illegal immigrants to pay in-state tuition to attend...