WASHINGTON — Seeking a new generation of leaders, social conservatives are looking for a lot more than opposition to gay marriage and abortion.

An annual summit of faith leaders and conservative activists gave a platform to a new wave of Republican leaders, who derided President Barack Obama’s health care law, his steering of the economy and foreign policy along with a more traditional litany of social issues.

In what amounted to an audition, Senate Republicans like Ted Cruz of Texas described a nation teetering on “the edge of a cliff” while Rand Paul of Kentucky said U.S. foreign policy needed to stop a “war on Christianity.” Mike Lee of Utah said the nation’s economic problems represented “moral threats” to the stability of families.

“We can’t stop talking about the importance of our values and our culture,” said Sen. Marco Rubio of Florida, who joined a parade of prominent GOP leaders at the Values Voter Summit on Friday. “We can’t stop talking about them because the moral well-being of our people is directly linked to their economic well-being.”

Organizers said Saturday that Cruz won the event’s straw poll of possible 2016 presidential candidates with 42 percent, followed by Dr. Ben Carson and former Pennsylvania Sen. Rick Santorum with 13 percent. Paul and Rubio placed fourth and fifth, respectively, offering an informal popularity contest among the roughly 2,000 attendees.

Social conservatives gathered at the summit as congressional Republicans sought agreement with Obama on a way to end the government shutdown, now in its 12th day, and avoid an economic default. Few in the audience expressed interest in backing down from efforts to defund or delay the nation’s health care law, a primary driver of the impasse, and said they wanted congressional Republicans to bring down the nation’s debt.

Marlene Kellett of Columbia, Md., said Republicans needed to hold firm in their opposition to the so-called Obamacare law. But she expressed pessimism that Republicans would make progress.

“I’m very opposed to Obamacare — it’s a disaster,” Kellett said. “But I’m not feeling very positive about (the impasse). So often the Republicans cave, and they can’t seem to get what they want.”

Adrienne Grizzell of Lexington, Ky., said the accumulation of nearly $17 trillion in debt — the source of a debate over whether to raise the nation’s borrowing limit — is too often shrugged off. “It’s as if, ‘No, it’s not a problem, let’s keep spending,”’ she said. “Nobody is saying, ‘OK, we’ve going to start spending less.”’

While social issues touched the hearts and minds here, speaker after speaker stressed pocketbook issues a year after Democrats vilified GOP presidential nominee Mitt Romney as being oblivious to the needs of middle-class families during tough economic times.

Cruz, whose speech was interrupted several times by immigration reform advocates, said Friday the health care law and Obama’s spending priorities had put the nation on the wrong track. “We have a couple of years to turn this country around, or we go off the cliff into oblivion,” he said.

Lee said economic issues such as a lack of economic opportunity, stagnant wages and spiraling housing costs represented “moral threats to families’ stability.”

Rubio said too many families are struggling to pay for child care and grappling with student loan debts. Paul devoted his remarks to foreign policy, describing attacks on Christianity in the Muslim world.

Santorum, who chased Romney for the GOP nomination during the 2012 primaries, previewed an upcoming holiday film, “The Christmas Candle,” released by his film company. Santorum recalled the early days of his presidential campaign, something he said, “that comes to mind every now and then, even today.”

To be certain, gay marriage and abortion got plenty of attention. Carson, a Maryland physician popular with conservatives, rejected the notion of a “war on women,” raised by Democrats, saying, “The war is on their babies.” He said marriage was a “sacred institution” that did not need a new definition.

Along the sidelines, conservatives said they were actively seeking a new group of conservatives to rally behind — and made clear that they don’t want capitulation.

“We don’t have enough Ted Cruzes and Marco Rubios,” said Jerry Skirvin, who runs a marketing firm in Lynchburg, Va. “We have too many John McCains and Lindsey Grahams,” he said, identifying two GOP senators often accused of seeking conciliation with Democrats.

The search also took place in private. Before the summit, Cruz and Paul sat down for separate closed-door meetings with a group of evangelical leaders, including Tony Perkins, the president of the Family Research Council, which sponsored the event, former presidential candidate Gary Bauer and Robert Fischer, a South Dakota businessman. The senators were joined by their wives during the session and discussed their faith and views on issues.