Nikki Haley, expressing confidence, says she has been here before.

Nikki Haley, in her final appearances before polls close in New Hampshire Tuesday night, rejected claims that Republican voters had already solidly united behind former President Donald J. Trump, and pledged not to end her 2024 presidential bid no matter how the state’s first-in-the-nation primary turned out.

“I didn’t get here because of luck,” she said at a polling site in Hampton, N.H., while flanked by supporters, including Gov. Chris Sununu, her top surrogate in the state. “I got here because I outworked and outsmarted all the rest of those fellas. So I’m running against Donald Trump, and I’m not going to talk about an obituary.”

Asked for her response to Mr. Trump’s remarks at his rally a day earlier, in which he suggested she would likely drop out after New Hampshire, she smiled.