CHARLESTON, S.C. – Avery and Susan Burns don’t like the immigration-reform bill in the U.S. Senate one bit. “People come here illegally, and now we’re giving them the red carpet,” grumbled Avery, a 71-year-old doctor, climbing the steps of the public library on a recent morning. His disgust is making him reconsider his support for home-state Sen. Lindsey Graham, the only Republican sponsor of the bill who is up for reelection in 2014. Yet Susan said she’d still vote for Graham because he’s a “strong Republican,” recalling his leadership during former President Clinton’s impeachment. The retired couple’s reaction shows why...