As Ambassador Nikki Haley climbs in polls at New Hampshire, she is telling President Trump to “bring it” in response to him directing his attention away from Governor DeSantis and toward her.

A new Suffolk University, USA Today, and Boston Globe poll found that Ms. Haley had surpassed Mr. DeSantis in the 2024 GOP presidential primary race there and is now second behind Mr. Trump.

The poll found that Mr. Trump enjoys 49 percent support, while Ms. Haley is at 19 percent and Mr. DeSantis is at 10 percent. Governor Christie was fourth with 6 percent support. No other candidate received more than 5 percent support.

Mr. Trump has, in turn, directed his attention toward Ms. Haley and away from his perennial punching bag, Mr. DeSantis, criticizing Fox News for having supporters of Ms. Haley as guests on the network.

“Fox has totally given up on Ron DeSanctimonious, and is on their next ‘journey’ pushing Nikki ‘Birdbrain’ Haley, who stated loudly and often that ‘President TRUMP was a GREAT President, and I would NEVER run against him,’” Mr. Trump said in a Truth Social post. “Well, so much for that.”

In response, Ms. Haley told Mr. Trump to “Bring it” in a post, adding, “Love this. It means we are in 2nd and moving up fast.”

In the national polls, Ms. Haley has been rising steadily since late August. On August 22, the day of the first debate, Ms. Haley enjoyed 3.4 percent support in FiveThirtyEight’s national average of polls. As of October 5, that had risen to 7.6 percent.

In early-voting states, Ms. Haley’s rise has been more dramatic, with a Public Opinion Strategies and Citizen Awareness Project poll from late September finding that she enjoyed 11 percent support, up from 3 percent in August ahead of the first debate.

In South Carolina, Ms. Haley, a Palmetto State native, has risen to second place, trailing Mr. Trump by 31 points with 17 percent support, according to a recent Winthrop University poll.

“We continue to see Trump’s dominance for the nomination in South Carolina,” the Winthrop poll director, Scott Huffmon, said. “While a distant second, support for Nikki Haley has grown. Haley’s rise coincides with the continued slide of Ron DeSantis with his drop in national polls being mirrored in South Carolina.”

During Ms. Haley’s rise in the polls, Mr. Trump has done more than just call her “Birdbrain.” Earlier this month, Mr. Trump had a birdcage delivered to Ms. Haley’s hotel room in Iowa.