Once Governor Jan Brewer signs the bill into law gay couples could be refused service at restaurants, stores, or any other private business. A major issue however is how a business owner would establish a customer's sexual orientation.
Supporters of the bill claim that to force businesses to serve homosexuals would violate their First Amendment Rights, however opponents claim that the law creates second-class citizens in much the same manner that Jim Crow laws did for African American citizens... images of "No Coloreds" signs come to mind as we could very easily see signs reading "No Gays". Lawyers have argued that the law violates the Civil Rights Act of 1964 and the Civil Rights Act of 1991.
A similar law was blocked in Kansas earlier this month when Republicans in the state legislature supported opposition Democrats arguing that the law legalized discrimination. It would seem that this Arizona law may be destined for the U.S. Supreme Court.