SB 1062 allows people to claim their religious beliefs as a defense against claims of discrimination. Backers cite a New Mexico Supreme Court decision that allowed a gay couple to sue a photographer who refused to document their wedding, even though the law that allowed that suit doesn't exist in Arizona.
Sen. Al Melvin, a Republican who is running for governor and voted for the bill, said he was disappointed by the veto.
"I am sorry to hear that Governor Brewer has vetoed this bill. I'm sure it was a difficult choice for her, but it is a sad day when protecting liberty is considered controversial," Melvin said.
Democrats said it was a veiled attempt to legally discriminate against gay people.
Rep. Ruben Gallego, D-Phoenix, said he would remain vigilant of other legislation that could also target gays.
"The effect is that again we got a black eye," Gallego said. "But it also shows that Arizona can stand united"
The Center for Arizona Policy helped write the bill and argued it was needed to protect against increasingly activist federal courts and simply clarifies existing state law. It accused opponents of mischaracterizing the bill and threatening boycotts of Arizona.
"It is truly a disappointing day in our state and nation when lies and personal attacks can overshadow the truth," said Cathi Herrod, the leader of the group.
Similar religious-protection legislation has been introduced in Ohio, Mississippi, Idaho, South Dakota, Tennessee and Oklahoma, but Arizona's plan is the only one that has been passed by a state legislature. The efforts are stalled in Idaho and Kansas, and was withdrawn in Ohio Wednesday among concerns it would have unintended consequences.
The push in Arizona comes as an increasing number of conservative states grapple with ways to counter the growing legality of gay marriage. Arizona has a ban on gay marriage.
Federal judges have recently struck down those bans in Utah, Oklahoma and Virginia, but those decisions are under appeal.
On Wednesday, a federal judge declared Texas' ban on gay marriage unconstitutional, but left it in place until an appeals court can rule on the case.
Associated Press reporter Astrid Galvan in Phoenix, Brady McCombs in Salt Lake City and Jesse Holland in Washington contributed.
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