This is from Kris Kobach, who helped draft the law, in our symposium on the issue:

Arizona epitomizes what every Republican — indeed, every American — should embrace: attrition through enforcement. For years, the open-borders crowd has claimed that the only two responses to illegal immigration are amnesty or mass roundups. That is nonsense. Attrition through enforcement presents an effective third option that respects the rule of law. By stepping up the enforcement of immigration laws through state-level action, Arizona has induced thousands of illegal aliens to self-deport. Need proof? In early 2008, after Arizona’s E-Verify law went into effect, the neighboring Mexican state of Sonora sent a delegation to the Arizona legislature to protest that Arizona was causing too many Mexican nationals to return to Mexico too quickly, overwhelming the housing stock and public infrastructure of Sonora.