Two under-the-radar Republican candidates are surging in polls after the debate

One candidate who didn't qualify for the main Republican presidential debate last Thursday - and another who just made the cut - are suddenly surging in several new polls.

In a new poll of New Hampshire Republican primary voters from the Boston Herald and Franklin Pierce University published on Tuesday, both Ohio Gov. John Kasich and former Hewlett-Packard CEO Carly Fiorina (R) leaped several spots.

Kasich flew up to third place, behind only real-estate magnate Donald Trump and former Florida Gov. Jeb Bush. And Fiorina jumped to fifth place among the 17 major candidates, with 9% of likely voters responding that they'd support her if the election were held today.

Kasich now sits 6 points behind Trump, the current front-runner, and just 1% below the second-place Bush. Overall, he has jumped 11 points in New Hampshire since a March poll conducted by FPU.

Kasich's late entrance into the presidential race helped him snag the last spot in the debate in Cleveland last week. Buoyed by a cheering hometown crowd, Kasich successfully articulated a compassionate, conservative message, standing by his support for the Medicaid extension under Obamacare and saying why he'd support his daughter if she were gay.

"Kasich is killing it. Hopeful. Uplifting. Optimistic. And he has an appeal to those who think the GOP doesn't care," Ari Fleischer, former press secretary in President George W. Bush's White House, tweeted.

Kasich's apparently rising level of support could be a problem for the other similar candidates like Bush and New Jersey Gov. Chris Christie (R), both of whom are putting many of their eggs in the Granite State.

Though Iowa voters tend to be far more religious and conservative, and tend to nominate candidates who reflect those values - former Arkansas Gov. Mike Huckabee (R) and former US Sen. Rick Santorum (R-Pennsylvania) won in 2008 and 2012, respectively - winning in New Hampshire has traditionally helped candidates build momentum and fundraise into the later voting contests.

Fiorina's support, meanwhile, is up significantly from a Monmouth University poll taken in mid-July that showed her in ninth place with 3% support among New Hampshire GOP primary voters.

Fiorina also jumped to sixth in a new post-debate Suffolk University poll of Iowa Republican voters, and fifth in a new Public Policy Polling poll of Hawkeye State voters released on Monday.

Many analysts ruled that the former HP executive - who has never held elected office - had one of the strongest performances of the early debates, providing quick, smooth answers to questions that occasionally flustered her peers.