Less than 24 hours before the candidates’ deadline to qualify for Fox News’s debate, two polls released on Monday show Donald J. Trump with a statistically significant lead over the rest of the field and Gov. John R. Kasich of Ohio squeaking into the top ten.

One of the surveys, a Fox News poll, is only one of five national polls that the network’s “decision desk” will use to determine who makes the debate in Cleveland on Thursday evening, and the other, a WMUR poll conducted by the University of New Hampshire, will not be a deciding poll for the debates.

But the numbers are notable.

In the Fox poll, Mr. Trump, the bombastic real estate developer, receives 26 percent of self-identified primary voters, a rise from 11 percent a month ago. Mr. Trump is getting the most support of any candidate since Fox News started polling the primary in December 2013, Fox News officials said.

Jeb Bush, the former Florida governor, is second with 15 percent. Gov. Scott Walker of Wisconsin got 9 percent, followed by former Ben Carson, who received 7 percent, and Senator Ted Cruz of Texas tied with Mike Huckabee at 6 percent.

Rounding out the top ten are Senators Marco Rubio and Rand Paul, Gov. Chris Christie of New Jersey and Mr. Kasich.

Among the Democrats, Hillary Rodham Clinton received 51 percent, Senator Bernie Sanders received 22 percent and Vice President Joseph R. Biden Jr., who is said to be considering entering the race, got 13 percent.

In the New Hampshire poll, Mr. Trump holds 24 percent of the vote; Mr. Bush, his nearest challenger, clocks in with 12 percent.

But even New Hampshire’s professional voters appear to be taking the Trump candidacy with a grain of salt. Twenty six percent of those surveyed think Mr. Bush will actually win the primary; 25 percent think Mr. Trump will win, while 8 percent give the nod to Mr. Walker, who is running a close third to Mr. Bush.

Mr. Walker registers the highest net favorable rating — 52 percent view him positively while just 14 percent view him negatively. Mr. Trump wins almost as high a favorable rating, at 51 percent, but 40 percent of voters view him negatively.

Though only one of the polls will be used to determine the lineup, the top tens are consistent in each, with Carly Fiorina, Rick Santorum, Rick Perry, Gov. Bobby Jindal of Louisiana, George E. Pataki, Senator Lindsey Graham of South Carolina and Jim Gilmore left outside looking in. Those who do not make the prime time debate will participate in a separate candidate forum at 5 p.m. on the same day.