Even though Massachusetts Sen. Elizabeth Warren has declared that she is not running for president in 2020, her shadow looms over the New Hampshire Democratic presidential primary, according to a new Suffolk University poll of New Hampshire voters. President Donald Trump dominates the Republican side.

Meanwhile, incumbent Republican Gov. Chris Sununu is leading potential Democratic challengers as he seeks reelection in November.

Potential Democratic candidates

Active campaigning in New Hampshire is still a year and a half away, but were Warren to enter the fray, she would lead among probable Democratic primary voters. In a theoretical field of candidates, Warren was the choice of 26 percent of respondents, followed by former Vice President Joe Biden (20 percent), Vermont Sen. Bernie Sanders (13 percent), New Jersey Sen. Cory Booker (8 percent), California Sen. Kamala Harris and former Massachusetts Gov. Deval Patrick (4 percent each). New York Sen. Kirsten Gillibrand and former Virginia Gov. Terry McAuliffe (2 percent each), with 18 percent undecided.

“Elizabeth Warren overtakes the entire field in her neighboring state, if she decides to run,” said David Paleologos, director of the Suffolk University Political Research Center in Boston. “The biggest losers are Sanders, Patrick and Harris, whose respective overlaps of political philosophy, geography and gender, rotate to Warren.”

With Warren out of the mix, Biden led Sanders 30 percent to 25 percent, with Booker at 10 percent; Patrick, 8 percent; Harris, 6 percent; Gillibrand, 3 percent; and McAuliffe, 2 percent, with 12 percent undecided.

“For someone who hasn't visited New Hampshire in over a year, Joe Biden’s popularity is strong and steady,” said David Paleologos, director of the Suffolk University Political Research Center in Boston. “What is perhaps surprising is that Bernie Sanders—who secured 60 percent of the New Hampshire Democratic primary vote in 2016—is retaining less than half of that support two years later.”

Candidates like Biden, McAuliffe, Gillibrand and Booker lost a modest 1 in 5 of their voters to Warren. But Patrick, Harris and Sanders lost more than one in three of their core supporters.

Republican matchups

Some prominent Republican names were tested against Donald Trump in hypothetical one-on-one Republican primary scenarios, and in all four tests, Donald Trump showed overwhelming strength.

Trump led 2012 Republican presidential nominee Mitt Romney 63 percent to 28 percent among probable New Hampshire GOP primary voters. In other matchups, voters preferred Trump 66 percent to 23 percent against Florida Sen. Marco Rubio; 68 percent to 23 percent over Ohio Gov. John Kasich; and 72 percent to 15 percent against Arizona Sen. Jeff Flake.

Gubernatorial race

With the November election for governor on the horizon, there are two Democrats vying in the primary. Sununu led Democrat Steve Marchand, former mayor of Portsmouth, 49 percent to 25 percent, with Libertarian Jilletta Jarvis at 4 percent and 21 percent undecided. In a matchup against Democrat Molly Kelly, a former state senator, Sununu led 48 percent to 27 percent, with Jarvis at 4 percent, and 21 percent undecided.

The gun issue

Granite State voters, asked about ways to prevent gun violence, preferred banning the sale of military-style assault weapons (41 percent), implementing a 48-hour waiting period for all gun licenses (17 percent), or arming teachers who complete training (12 percent). Nearly one in five (19 percent) said no new law will help. Even among gun-owning households, the number one response was banning military-style assault weapons (31 percent), although 27 percent said no new law would help.

History of Suffolk research in New Hampshire

In the 2016 presidential election, the final Suffolk University poll predicted a 42 percent-42 percent dead heat between Hillary Clinton and Donald Trump. Clinton won by 0.4 percent. In the 2014 New Hampshire general election, the final Suffolk University poll predicted a 3-point win for Democratic Sen. Jeanne Shaheen over Republican Scott Brown; Shaheen won by 3 percent.

Methodology

The statewide survey of 800 likely general election voters was conducted April 26 – April 30, 2018, using live telephone interviews and a split sample of landline and cell phone numbers. The margin of error is +/- 3.5 percentage points at a 95 percent level of confidence. The margin of error on the subset of 295 likely Democratic presidential primary voters is +/- 5.7 percentage points. The margin of error on the subset of 315 likely Republican presidential primary voters is +/- 5.5 percentage points. Marginals and full cross-tabulation data are posted on the Suffolk University Political Research Center website. For more information, contact David Paleologos at 781-290-9310, dpaleologos@suffolk.edu.