In a race where early state polling can decide whether a candidate is allowed to debate, Governor Christie surged to second place in the latest polls out of New Hampshire while two South Carolina natives, Governor Haley and Senator Scott, are stalling out in the Palmetto State.

Beyond the perennial importance of early primary states being used as stepping stones to late campaign success, early states are taking on increased importance in this year’s GOP presidential primary.

The Republican National Committee is requiring candidates to meet certain polling requirements in order to participate in the upcoming debates. For the first debate, candidates have to poll at 1 percent in three national polls or two national polls and an early state poll. For the second, candidates must poll at 3 percent. The early states that count are Iowa, New Hampshire, South Carolina, and Nevada.

New survey data from early states show that, while Mr. Trump holds a big lead, candidates are investing heavily to be the runner-up and to boost their numbers.

An Emerson College survey released Tuesday found that Mr. Christie had jumped to second place in New Hampshire, taking what was Governor DeSantis’s spot behind Mr. Trump.

According to the survey, Mr. Trump leads with 49 percent support, followed by Mr. Christie at 9 percent, Mr. DeSantis at 8 percent, Mr. Scott at 6 percent, and Governor Burgum at 4 percent.

“DeSantis has been the alternative to Trump in Emerson polling this presidential cycle,” pollster Spencer Kimball said. “This is the first time we have seen DeSantis drop out of second place in our polling, and fall back into the pack of candidates.”

New survey data are also shining a light on South Carolina, an early state unique this cycle for having two natives running for the GOP nomination — Mr. Scott and the state’s former governor, Ms. Haley.

The survey found that, despite the two South Carolina natives being in the race, Mr. Trump has expanded his lead there since the pollster, National Public Affairs, released its June survey. Mr. Scott is a native of North Charleston and Ms. Haley is from Bamberg.

In the survey, Mr. Trump posted 45 percent support, up 4 points from the June survey. Mr. DeSantis was second at 13 percent support, down 5 points from June.

Ms. Haley and Mr. Scott were tied for third place at 11 percent support. For Ms. Haley this represented a 1 point drop in support since June; for Mr. Scott it represented a 1 point gain. Mr. Christie and businessman Vivek Ramswamy also both saw their support increase, to 7 percent and 5 percent respectively.

Another finding of the National Public Affairs survey that confirms something apparent in national trends is that, for some voters, the charges against Mr. Trump don’t matter. The survey found that 34 percent of respondents said the indictments “solidified” their support for him, and they convinced 2 percent to support him.

For comparison, 4 percent said that the news convinced them to no longer support Mr. Trump and 37 percent said the indictments did not change their mind “one way or another.”

In Iowa, the latest survey from J.L Partners and the Daily Mail also found Mr. Trump with a commanding lead, at 43 percent support. Mr. DeSantis was second at 17 percent and Mr. Scott was third at 11 percent support.

Nevada is the only early state where there is no recent polling data available for the GOP primary. The state’s nomination process is in flux, with a new state law requiring the state, which has traditionally held caucuses, to hold a primary election.

The state’s GOP is also planning on holding a caucus, which it says is going to be the actual nominating competition where voters decide which candidate will receive the state’s delegates. This means the primary will probably not have any bearing on the nomination process.

On Monday, Nevada Republican officials announced that it would hold its caucus on February 8, a few weeks before the February 24 South Carolina primary and a few weeks after the January 15 Iowa caucus.