WASHINGTON — Conservative Republicans claimed victory this week in the Supreme Court ruling on religious freedom and the White House’s acceptance that an immigration overhaul won’t happen this year. Today’s victories could haunt the GOP in two years’ time, as the party’s presidential nominee looks for much-needed support among women and Hispanics in the 2016 election.

With no movement on immigration legislation, a new crop of Republican presidential candidates will be asked to outline their own plans for resolving a vexing issue that is a top priority for many Hispanic voters and concerns business leaders who traditionally support the GOP. And Monday’s high court decision granting some companies religious exemptions from providing contraception coverage gives Democrats a peg to reopen a debate on women’s health that tripped up Republicans in the last election.

Additional Photos This June 25, 2014 file photo shows New Jersey Gov. Chris Christie speaking in Haddon Heights, N.J. Christie will be in Maine Tuesday to campaign for Gov. Paul LePage. This May 31, 2014 file photo shows Sen. Ted Cruz, R-Texas speaking in New Orleans, La. This photo taken June 30, 2014 shows the Supreme Court in Washington. Conservative Republicans claimed victory this week in the Supreme Court ruling on religious freedom and the White Houses acceptance that an immigration overhaul wont happen this year. Todays victories could haunt the GOP in two years time, as the partys presidential nominee looks for much-needed support among women and Hispanics in the 2016 election.

For more moderate Republican presidential hopefuls, both developments present a familiar conundrum: how to stake out positions conservative enough to appeal to the voters who dominate Republican primaries while not turning off those who could be swayed in the general election. It’s a challenge 2012 Republican nominee Mitt Romney was unable to navigate — he tacked to the right as he outlasted his primary rivals, but could not compete with President Barack Obama among women and Hispanic voters on Election Day.

The struggle to strike the right balance was evident immediately. Chris Christie, the typically outspoken New Jersey governor, ducked questions this week about his view of the Supreme Court’s decision on contraception.

“Why should I give an opinion on whether they’re right or wrong?” Christie said during an interview Tuesday on CNBC. “In the end of the day, they did what they did. That’s now the law of the land unless people in the elected branches try to change it.”

Such efforts to avoid the question will be challenged by 2016 hopefuls on GOP’s right flank eager to talk about the high court ruling as a victory for religious liberty and the end of the legislative debate on immigration as a win for those who equate creating a path to citizenship for people living in the U.S. illegally with amnesty.

For potential candidates such as Texas Sen. Ted Cruz — he quickly cast the Supreme Court decision as a “repudiation” of Obama — doubling down on those positions may be the best way to rally support in the early voting states of Iowa and South Carolina, where primary voters tilt more conservative.

Further complicating matters: the elections that arrive this November. With midterm turnout traditionally low and some of the most competitive races taking place in conservative-leaning states, GOP candidates are likely to rally behind issues that will pay off with a win this year rather than shaping a message for the more diverse electorate faced by Republican presidential contenders.

Following Romney’s loss to Obama, national Republicans called for the party to be more inclusive and placed particular emphasis on reaching out to women and Hispanics. The GOP concern reflected the reality of shifting demographics and public opinion.

On immigration, surveys show that the majority of Americans favorably view a pathway to citizenship for the more than 11 million people living in the country illegally. The issue resonates particularly strongly with Hispanics, one of the fastest-growing groups of voters in the U.S., and has broad support from the business community and evangelicals, groups that traditionally back Republicans.

In 2012, Hispanics comprised 10 percent of the electorate, more than in any other year. More than 70 percent of those voters backed Obama.

Women made up just over half of the electorate in the 2012 presidential campaign and 55 percent of them voted for Obama. Polls show a large majority of women think for-profit companies should be required to cover the cost of birth control. A Gallup survey conducted in May also found that 90 percent of Americans, including 88 percent of Republicans, see the use of birth control as morally acceptable.

As White House hopefuls plot their strategies for 2016, some Republican operatives say the key to increasing the party’s appeal with Hispanics and women rests not with finding an attractive message on potentially divisive issues, but on focusing squarely on the economy.

“Part of the challenge here is how do we effectively engage on the No. 1 issue,” said Republican pollster David Winston, noting that GOP congressional candidates won the majority of female voters in the 2010 midterm elections when the economy was a central focus of the campaigns.

But Alice Stewart, a Republican strategist who worked for conservative 2012 candidates Rep. Michele Bachmann of Minnesota and former Pennsylvania Sen. Rick Santorum, said the party can’t afford to sit back and allow Democrats to define issues that could create a wedge within the GOP.

“The key is to get out in front and make sure we drive the right message instead of letting the left define it,” Stewart said. “We learned that lesson in 2012.”

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