After her breakout performance at the first debate, the former South Carolina governor has gained attention from Republican voters and donors and is moving up in the polls.At a campaign event at a scenic country club in Portsmouth, N.H, on Thursday, James Peterson, a businessman, thrilled an audience when he stunned Nikki Haley with a question she said she had never heard before, and which cut straight to the point: 100 years from now, how do you think history will remember Donald Trump?“I always say, ‘I’ve done over 80 town halls in New Hampshire and Iowa — that’s all the debate prep I need,’ but you take it to a whole new level,” Ms. Haley said to a roar of laughter from roughly 100 Rotary Club members and their guests.She then took a quick beat before diving into a measured, yet sharpened, critique of Mr. Trump and his administration — the good, the bad, and with some subtlety, the ugly.“Time does funny things. My thought will be that he was the right president at the right time,” she said, later making clear, “I don’t think he is the right president now.”Such a thorny question might be just the type of preparation Ms. Haley, 51, the former South Carolina governor and United Nations ambassador, is looking for as she heads into the next Republican presidential debate on Wednesday with real momentum — and as the likely focus of political attacks.After her last performance on the national debate stage, in which she made a strong general election pitch and tangled with opponents on foreign policy, climate and abortion, Ms. Haley has seen gains in the polls, a rush of volunteers and swelling interest from early-state voters.Recent surveys have her running third in Iowa and New Hampshire and second in her home state of South Carolina. One CNN survey showed Ms. Haley beating President Biden in a hypothetical general-election matchup.Some of her top fund-raisers said donors who had been waiting on the sidelines for a Trump alternative to emerge were coalescing behind her. Former Gov. Bruce Rauner of Illinois, a top giver to her rival, Gov. Ron DeSantis of Florida, has transferred his allegiance to Ms. Haley.Another major backer, Eric J. Tanenblatt, an Atlanta businessman who has hosted three fund-raisers for Ms. Haley since March, said the excitement around her candidacy has increased significantly in recent weeks.“When she was here last week, we didn’t have to call people, people were calling us,” he said. He noted that the size of her events have grown, “each one bigger than the one before.” He added of his most recent gathering: “We had to turn people away — it is a good problem to have.”But even as Ms. Haley looks to replicate her debate success next week, the 2024 presidential race still appears to be Mr. Trump’s to lose. And with voters and donors starting to pay more attention, her rivals are likely to as well.Since the last debate, Ms. Haley has mostly split her time between New Hampshire and South Carolina while also making up ground in Iowa. She has continued to burnish her foreign policy credentials, criticize Republicans on spending — which played well in the first debate — and call for a change in generational leadership.On a farm last week in Grand Mound, Iowa, she drove a corn combine and spoke of the need to fix the legal immigration system to address farmers’ labor shortages against a backdrop of gleaming green tractors and American and Iowa flags. But she also pledged to defund sanctuary cities and send the military into Mexico to tackle drug cartels.In a packed auditorium at St. Anselm College in Goffstown, N.H., on Friday, Ms. Haley laid out her economic priorities, including eliminating the federal gas and diesel tax, ending green energy subsidies, overhauling social security and Medicare for younger people and withholding the pay of Congress members if they fail to pass a budget.She criticized both Republican and Democratic presidents for increasing the debt but reserved her toughest broadsides for China and Mr. Biden, whom she accused of plunging the nation into “socialism” and enlarging government, saying he was pouring money into social and corporate welfare programs that she argued were hurting the poor “in the name of helping the poor.”Ms. Haley rode a corn combine during a farm tour in Grand Mound, Iowa, last week.Rachel Mummey for The New York TimesHer appearances lately have drawn in moderates, independents and even some Democrats who say they like her fresh face and appeals to common sense and reason. “I like her fast thinking and proactive ideas,” said Nancy Wauters, 67, a retired medical office support staffer and an independent voter who went to see Ms. Haley speak at a Des Moines town hall last week after being impressed by her performance in the first debate.But swaying Trump die-hards who have continued to rally behind the former president has been more difficult. “I like Nikki Haley a lot,” said Barbara Miller, 64, a retired banker, at Ms. Haley’s event in Portsmouth. “But I just feel that Donald Trump is the stronger, more electable candidate.”When another voter at the country club in Portsmouth pressed Ms. Haley on how she would overcome his advantage, Ms. Haley said she expected the field to winnow after the contests in Iowa and New Hampshire and to come to a “head-to-head” matchup in her home state of South Carolina.Mr. Trump missing the first debate and now possibly the second was a mistake, she said.“You can’t win the American people by being absent,” she said. 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