Nelson Warfield, a conservative consultant who advises Mr. Scott, said that many conservatives applauded the intent of the law, to permit business owners to follow their religious conscience. But the battle over the law was lost, he said, as soon as it moved from being a fight over religious freedom to one of “personal dignity.” He said laws like the one vetoed in Arizona would certainly be embraced by some Republican presidential candidates in 2016 during the primaries, but would be toxic for a Republican candidate in a general election.

“You can bet your last dollar somebody will run on it for the nomination next time,” he said, referring to the Republican presidential battle of 2016. “But the issue was framed in the worst possible way for those people who are supporters of the bill,” he said. “It became about human rights and human dignity and not religious conscience. As soon as it shifted from a debate about religious conscience to a respect for human dignity, it was a loser.”

The defeat in Arizona could have implications for conservatives in other State Houses that are pushing similar legislation, including Missouri, Mississippi, Oklahoma and Kansas, where an even stronger proposal to permit discrimination on religious grounds appeared to be dead this year but seems likely to be revived. Already on Thursday the bill in Mississippi, which had passed the State Senate, was placed on delay by the House Judiciary Committee, which was scheduled to consider it that day.

“For this year, we are hopeful, but every state has its own politics,” said Sarah Warbelow, the state legislative director for the Human Rights Campaign, a gay lobbying organization. “We’re mobilizing our members and supporters to fight in these states.”

The divisions surrounding this issue were reflected in the careful deliberations Ms. Brewer undertook before deciding on her veto and in the tentativeness of Mr. Scott, who is facing a tough re-election campaign, in dealing with the question in a morning television interview. “In Florida, we are focused on economic growth, and not on things that divide us,” he said later in the day in a statement urging its veto.