New Jersey Gov. Chris Christie’s rise in New Hampshire is finally starting to cut into some of his competitors, most conspicuously former Florida Gov. Jeb Bush. 

Christie, who’s enjoyed a modest surge in the state through relentless campaigning, got some further good news on Tuesday: A new Quinnipiac national poll showed him just ahead of Bush. (A CNN/ORC poll out Wednesday also showed Christie ahead of Bush, 5 percent to 3 percent.) The New Jersey governor is already polling ahead of his establishment rival in the first-in-the-nation primary state of New Hampshire, pipping Bush in the RealClearPolitics average of state polls, 6 percent to 4 percent.

Bush added to the tension on Tuesday when, during a campaign event in Berlin, in New Hampshire’s far north, he contrasted his record with Christie’s in the latest sign of their emerging rivalry. “I would say it’s the record of accomplishment — my record in Florida compared to his,” Bush said, going on to say that he's a “reform-minded conservative that got to do big things,” while Christie has “had credit downgrades. We led the nation in job growth. New Jersey hasn’t done as well.”

The stakes for Bush and Christie are clear: Both men have made succeeding in New Hampshire a do-or-die prospect, with no clear path forward if they don’t finish at or near the top. And both are vying for the same pool of voters: mainstream conservatives who aren’t comfortable with Donald Trump or Ted Cruz.

“I think Christie has the chance to solidify that group of voters,” said New Hampshire Senate Majority Leader Jeb Bradley, one of several prominent Granite State politicians to endorse Christie.

In a further sign of potential trouble for Bush, his voters seem to be showing a “curiosity” toward Christie, noted Matt Mayberry, vice chairman of the state Republican Party — especially in the weeks since the New Jersey governor was endorsed by Renee and Dan Plummer, a pair of influential New Hampshire activists. 

Over the weekend, Bush and Christie both campaigned around the state, holding dueling, jam-packed events just a short distance from each other and at about the same time. “A lot of people went to Christie down the street and literally walked down the four blocks for Jeb Bush,” Mayberry said.

On Saturday, Bush held four events while Christie — who has held more events in New Hampshire than anyone else in the GOP field, and often boasts about it — held three. Christie went on to campaign for two more days in the state and Bush returned for more events on Tuesday.

If Bush’s aides are reluctant to acknowledge the growing threat from Christie, the New Jersey governor’s are not: His staff eagerly points out every sign that their candidate is beating their better-funded rival in New Hampshire. “Every single poll since Thanksgiving has shown Christie ahead there,” said Mike DuHaime, Christie’s main political adviser. 

“I think you’re down to three that reasonably have a path: us, Bush and [Ohio Gov. John] Kasich,” another of Christie’s top campaign strategists said, noting his rise in various polls. “We feel pretty good about that.”

Still, Bush’s war chest dwarfs Christie’s, even after the former Florida governor’s super PAC has spent $50 million in a vain effort to move his numbers. In the third quarter of 2015, Bush's official campaign raised $13 million, while his super PAC and supporting political action committees, as of midyear, had raised $108 million. By comparison, Christie’s campaign,in the third quarter, raised just over $4 million, while his super PAC raised had $14.4 million through June.

Christie’s operation in New Hampshire is also smaller than Bush’s. He has just four paid staffers and one office, compared with Bush’s 20 staffers, four regional offices, and one headquarters.

The Bush campaign insists, moreover, that it has no special focus on Christie in New Hampshire but is using its December ad spending in the state to highlight Bush’s record on national security — a topic the New Jersey governor, a former prosecutor, has sought to make his own.

“With respect to any of the other candidates, including Christie, over the next 40-plus days, these records are going to be examined and litigated, and we are entirely confident with respect to the outcome that once that takes place, Jeb will be the obvious choice, and that includes a good showing in New Hampshire,” a person close to Bush said.

Others in the Bush camp said that donors have expressed concern over their candidate’s lack of movement in national polls. But campaign officials have moved to stop any major defections by showing donors that Bush is close to Marco Rubio in Iowa based on the latest Des Moines Register poll. And they noted that Bush is at 10 percent — essentially tied with Christie, Rubio and Cruz — in New Hampshire, according to a recent Franklin Pierce/Boston Herald poll.

Still, Bush campaign staffers haven’t refrained from taking a few shots at Christie. 

Tim Miller, Bush’s communications director, noted that he’s tweeted similar pokes at other candidates in the field — denying his gibes represent any kind of particular concern about Christie.

“I’ve been aggressively shaming all the other candidates for not standing up to Donald Trump. It is most of my feed for today if you look at it,” Miller wrote in an email, adding, “I feel no tensions towards Christie.”