Haley and DeSantis Take Leading Roles in Tense G.O.P. Debate

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The third Republican presidential debate devolved at times into brutal personal attacks as the five candidates onstage tried to discuss high-minded issues from the fate of Social Security to the role of America abroad between cutting asides and provocative insults.

The debate in Miami came a day after voters across the country rebuked the Republican Party, especially over abortion rights. But that issue, which drove voters to the polls in Virginia, Ohio, Kentucky and elsewhere on Tuesday, did not appear until an hour and 40 minutes in.

Once it did, the candidates showed the party’s divide. Senator Tim Scott of South Carolina emphatically expressed support for a federal ban on abortion after 15 weeks of pregnancy. Chris Christie, the former New Jersey governor, said it should be up to the states. The entrepreneur Vivek Ramaswamy spoke of “sexual responsibility for men,” suggesting that widely available paternity tests could be used to force men to take responsibility for pregnancies that should not be terminated.

And Nikki Haley, the former governor of South Carolina, sought a conciliatory position.

“I don’t judge anyone for being pro-choice, and I don’t want them judging me for being pro-life,” she said, adding, “Stop the judgment. We don’t need to divide America over this issue anymore.”

Voters in Iowa will cast the first votes of the Republican primary season in little more than two months, yet the debaters continued their competition for second place rather than training their fire on the prohibitive front-runner for the Republican nomination, former President Donald J. Trump.

For the third time, Mr. Trump did not bother to show up, instead counterprogramming at a simultaneous rally in nearby Hialeah, Fla. Aside from a few harmless jabs at Mr. Trump, the five candidates who did attend saved their harshest attacks for one another.

The most heated exchange came over the unlikely issue of TikTok. After Mr. Ramaswamy bragged about using the Chinese-owned social media network to broadcast his message, he turned to his nemesis, Ms. Haley, and mocked her daughter for using the app.

“Leave my daughter out of your voice,” she snapped, muttering into the microphone, “You’re just scum.”

But the debate did address weighty issues: whether a soaring budget deficit required a higher retirement age for access to Social Security and Medicare, how the United States should back Israel against Hamas and Ukraine against Russia, and how a president could immediately address the strain of inflation in everyday debate.

It even strayed into stultifying territory, as the conservative commentator Hugh Hewitt, one of the moderators, demanded to know exactly how many new ships should be added to the U.S. Navy to confront China.

But in the end, it was unclear how the five candidates onstage could catch Mr. Trump if they would not directly answer the question that started and ended the debate: Why should Republican voters choose them over Mr. Trump?