In the first poll focusing on the New Hampshire Republican presidential primary field since the first debate, Ambassador Nikki Haley and Governor DeSantis are tied, but no candidate appears to be able to approach President Trump’s lead.

The poll, conducted by NMB Research between August 26 and 31, asked likely GOP primary voters to name their first- and second-choice candidates. It found that Mr. Trump leads with 47 percent while Ms. Haley and Mr. DeSantis both have 10 percent support.

Businessman Vivek Ramaswamy and Governor Christie are at 8 percent, and Senator Scott is at 5 percent. No other candidate garnered 5 percent support or more.

As a second choice, Mr. Trump was listed by 9 percent, while Mr. DeSantis had 20 percent support, Mr. Ramaswamy had 18 percent, Ms. Haley had 15 percent, and Mr. Scott had 11 percent.

“Donald Trump has a significant lead on the Republican presidential primary ballot,” pollster Jim Hobart wrote in a memo summarizing the findings. “New Hampshire Republican presidential primary voters are focused on the economy.”

The survey, conducted on behalf of the Competitiveness Coalition, polled 800 likely GOP voters and had a margin of error of plus or minus 3.46 percent.

In terms of the issues that the voters were concerned about, inflation and cost of living were the most prevalent, with 28 percent saying it was their most important issue. Illegal immigration was the second most prominent issue, at 23 percent, followed by jobs and the economy, with 20 percent.

The survey’s results highlight the strength of Mr. Trump’s lead and come at a time when it’s looking less and less likely that any candidate will be able to challenge the former president.

A survey conducted before the debate by the Trafalgar Group, a Republican pollster, found that Mr. DeSantis was second at 11 percent, followed by Mr. Ramaswamy at 10 percent and then Messrs. Christie and Scott at 8 percent. Mrs. Haley was at 3 percent.

The shift in support between the Trafalgar Group survey and the NMB Research survey appears to show that debate performance may have affected levels of support but had little effect when it comes to Mr. Trump’s lead.

Ms. Haley, for one, had a breakout performance during the Republican debate and saw her poll numbers rise in the state at the expense of her rivals, except Mr. Trump. No candidate was able to gain ground on the former president.

As Mr. Trump continues to dominate New Hampshire, some Republicans in the state are pushing to see whether or not he can be disqualified from running for president under the 14th Amendment.

After raising this potential complication, a 2020 Republican candidate for Senate at New Hampshire and an attorney, Corky Messner, came into conflict with the state’s Republican Party.

In a recent op-ed for the New Hampshire Union Leader, Mr. Messner implored his fellow conservatives to seriously consider the question and allow the Supreme Court to decide whether Mr. Trump is disqualified from running under Section 3 of the 14th Amendment, which says someone who engaged in an insurrection can’t run for president. Mr. Trump’s detractors consider his role in the January 6 Capitol Hill protests to be insurrectionism.

“Everyone, Trump, Trump supporters, Republicans, Democrats, etc., should want the Supreme Court to render a decision on Section 3,” Mr. Messner wrote. “Trump and his supporters should be urging legal scholars who disagree with Baude, Paulsen, Luttig, and Tribe to write a thorough analysis of their opposite position.”

While the secretary of state of New Hampshire would not need any special permission to find that Mr. Trump is disqualified, such a move would almost certainly result in litigation. Based on the polls, it would probably cause a further rift in the New Hampshire GOP as well.