WASHINGTON (AP) -- It is a debate many Republicans hoped to avoid. But as the backlash intensifies over a so-called religious freedom law in Indiana, the GOP's leading White House contenders have been drawn into a messy clash that highlights the party's strong opposition to same-sex marriage and threatens to inject social issues into the early stages of the 2016 presidential primary season. The debate has also energized Democrats nationwide while exposing sharp divisions between Republicans and local business leaders who oppose a law that critics say allows business owners to deny services to same-sex couples on religious grounds. "It's been a tough week," Indiana Gov. Mike Pence said in a Tuesday press conference. He called for a legislative fix to address what he called a perception problem just five days after signing the bill into law. It is a huge moment for Pence, a Republican presidential prospect himself, who has become the public face of the contentious law. It is also a critical time for the Republican Party, which has recently played down its opposition to abortion rights and same-sex marriage to help attract more women and younger voters before the next presidential election. Polling suggests a majority of the American electorate supports gay marriage, but the most conservative Republicans do not. "It's a total head-scratcher," former Illinois Republican chairman Pat Brady said of the GOP presidential hopefuls who defended the law. "We're trying to attract voters and win elections. We can't scare people away." Yet the Republican 2016 presidential class overwhelmingly defended the new law, breaking with local business leaders in favor of conservatives across the country who cheered such laws as a necessary response to overreach by the Obama administration. "I think Gov. Pence has done the right thing," former Florida Gov. Jeb Bush said in a Monday radio interview. He said the law was "simply allowing people of faith space to be able to express their beliefs." Texas Gov. Rick Perry on Tuesday tweeted: "I stand with" Pence, and "Religious freedom is worth protecting." "We must stand with those who stand up for religious freedoms," former Arkansas Gov. Mike Huckabee said. Texas Sen. Ted Cruz, who announced his GOP presidential campaign last week, said the Indiana governor was "holding the line to protect religious liberty" in his state. Some economic-minded Republicans saw it another way. "It takes our eye off the really important things to most people in this country: jobs, the economy and our security," said Ronald Weisner, former finance chairman for the Republican National Committee. "That's probably not the best thing for our party as a whole." Last week, Pence signed the state Religious Freedom Restoration Act, giving heightened protections when businesses or individuals object on religious grounds to providing certain services. Critics of the law say the intent is to discriminate against gays. They fear, for example, that caterers, florists, photographers and bakers with religious objections to same-sex marriage will be allowed to refuse to do business with gay couples. Supporters of the law say it will only give religious objectors a chance to bring their case before a judge. Similar proposals have been introduced in more than a dozen states -- Arkansas, Georgia and North Carolina, among them -- patterned after the federal Religious Freedom Restoration Act of 1993. Nineteen other states have similar laws. North Carolina Gov. Pat McCrory, a pro-business Republican, has criticized such a proposal in his state, telling The Associated Press on Tuesday that he's yet to see evidence of a problem the bill purports to fix. Georgia's Republican House Speaker, David Ralston, said Tuesday "the case hasn't been made to me" that a state law is needed to address something already included in the Constitution. The U.S. Chamber of Commerce declined to respond to a request for comment Tuesday. The reaction to the law from the local business community based in the affected states has been negative. Some companies and organizations in recent days canceled future travel to Indiana or halted expansion plans in the state. Apple CEO Tim Cook wrote an op-ed opposing measures in Indiana and Arkansas, while retail giant Wal-Mart has said the proposal sends the wrong message. The leaders of pharmaceutical giant Eli Lilly and the business website Angie's List were among nine Indiana-based companies "deeply concerned about the impact it is having on our employees and on the reputation of our state," according to a letter they sent to Pence this week. Democrats were united in their opposition to the law. Hillary Rodham Clinton, expected to launch her Democratic presidential campaign in the coming weeks, tweeted last week, "Sad this new Indiana law can happen in America today." Democratic governors in Connecticut and Washington state and Washington, D.C.'s mayor have instructed their employees not to travel to Indiana on official business. ___ Associated Press writers Ken Thomas, Gary Robertson in Raleigh, N.C., Tom Beaumont in Des Moines, Iowa, Kathleen Ronayne in Bedford, N.H., and Bill Barrow in Atlanta contributed to this report.