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Donald Trump more likely than not will win the New Hampshire primary today. Both FiveThirtyEight forecasts give him more than a 2-in-3 shot to finish first. So let’s take a moment to appreciate what’s about to happen. Sure, Trump has some rough precedents, like Pat Buchanan, but the fact that he will probably win the first primary is … noteworthy.

But Trump still has a long-term problem: Our forecast projects him to receive a little less than 30 percent of the vote in New Hampshire. That might be enough to win — but mostly because the field is so big and the non-Trump vote so divided. So far at least, Trump has had a ceiling on his support. And there are signs of this ceiling in upcoming primaries in the South, which was supposed to be one of his strongest regions.

Trump has historically done well in Southern polls. The region has a lot of non-college educated, moderate white voters — a demographic group that is right in Trump’s wheelhouse. These voters used to be Democrats but over the past couple of decades have identified more and more as Republicans. They’re receptive to Trump’s populist pitch.

But four Southern-state polls that were taken mostly or completely after Trump’s second-place finish in last week’s Iowa caucuses show him barely leading or behind. (Weirdly, since Iowa, no one has conducted a poll of South Carolina, the next GOP contest after New Hampshire.)

Let’s start with Arkansas, where Mike Huckabee (who also has a tinge of populism to his pitch) served as governor. A Hendrix College poll conducted late last week found Trump tied for second with Marco Rubio at 23 percent, while Ted Cruz led both with 27 percent.

Georgia was supposed to be one of Trump’s stronger states. It was so Democratic during the 20th century that not a single Republican governor was elected. A poll from Landmark Communications in December had Trump towering over the field with 43 percent. The same pollster also found Trump ahead last week, but with 27 percent. He was less than 10 percentage points in front of Cruz and a surging Rubio, each with 18 percent.

Perhaps the best sign for Trump is that he still leads in Florida, the home state of Rubio and Jeb Bush. However, Trump’s 27 percent in a new Florida Southern College is the lowest percentage he’s received in any Florida pollin nearly three months. Meanwhile, the 20 percent going to Rubio is the best he’s done there since October. (Keep in mind that Florida is filled with retirees from Trump’s native Northeast.)

Finally, North Carolina — it’s a state that Trump should want to do well in: It’s right next to the second primary state, South Carolina, and like New Hampshire, North Carolina allows unaffiliated voters, whom Trump is expected to do reasonably well with, to vote in the Republican primary. Trump, though, received only 26 percent in the latest High Point University survey, barely ahead of Cruz and Rubio, with 22 percent and 20 percent, respectively.

Any one of these surveys in isolation wouldn’t be a big deal for Trump. Indeed, if Trump wins New Hampshire, his numbers could bounce back. But the fact that he’s under 30 percent in four Southern states suggests that he’s vulnerable in the region. And Trump probably can’t count on the same divided field he’s facing now once the race makes it to the Southern contests in early March (Arkansas and Georgia vote March 1; Florida and North Carolina vote March 15).

The road after New Hampshire — win or lose — will be rougher.