There's no clear Republican front-runner in the New Hampshire presidential nominating contest, while Hillary Clinton retains an overwhelming advantage among Democrats in the Granite State's first-in-the-nation primary.

Clinton's advantage over her potential Republican rivals has narrowed, however, and the general election in the battleground state looks increasingly competitive, according to a new Bloomberg Politics/Saint Anselm New Hampshire Poll.

The poll also shows that Senator Marco Rubio is rising while support for his fellow Floridian, former Governor Jeb Bush, has fallen off. Rubio and Bush both were the first choice of 11 percent of likely Republican primary voters in the poll, while Wisconsin Governor Scott Walker and Senator Rand Paul of Kentucky each scored 12 percent.

Read the poll questions and methodology here.

 
 

Clinton is the first choice of 62 percent of likely Democratic primary voters roughly nine months before the primary. That's her best showing since November and suggests a recent wave of influence-peddling allegations about her family's foundation as well as the controversy over her use of a private e-mail server while she was secretary of state haven't tarnished her with the party's base.

There are warning signs for Clinton in New Hampshire. Since the last poll in February, three of the top-polling Republican candidates—Bush, Paul, and Rubio—have moved into striking distance and are now within the poll's margin of error of tying her in hypothetical match-ups.

The poll, conducted May 2-6 by Washington-based Purple Insights, shows Bush and Rubio as Clinton's closest competitors in potential head-to-head contests. Both trail her by 2 percentage points. Paul is next, 3 percentage points behind her, followed by Walker, who trails Clinton by 6 points.

 
 
 
 
 
 
 
 

Clinton's closest New Hampshire primary competitor, Senator Bernie Sanders of neighboring Vermont, was the first choice of 18 percent of likely Democratic voters. Vice President Joe Biden was at 5 percent and former Maryland Governor Martin O'Malley at 3 percent. Neither Biden nor O'Malley have said they'll run.

“Clinton’s strength in the primary remains historic," said Purple Insights' Doug Usher. "But she’s facing the laws of political gravity among independent voters more quickly than her campaign might have hoped.”

 
 

Clinton's numbers with independent voters were destined to fall at some point, Usher said, as the campaign becomes more fully formed and intensely competitive. 

Among independent general-election voters in New Hampshire, Clinton is tied or nearly tied with Bush, Paul and Rubio. She does better against Walker with this group, leading 42 percent to 36 percent.

Rubio, who announced his candidacy April 13, more than doubled his level of primary support since the poll's last sample, in February. Bush, who isn't expected to formally announce until June, dropped five percentage points, his lowest level since the poll started tracking the state's voters in November.

Poll respondent Stephanie Korb, 57, a Republican dental assistant from Belmont, N.H., said she is leaning toward Rubio.

“He seems like a less offensive choice than the others,” she said. “I want to hear what the candidates want to do to turn this country around and you're not hearing that.”

Support for Paul and Walker have remained steady since February. Paul has formally announced his candidacy, while Walker is expected to hold off until June or later. 

Donald Trump was selected by 8 percent of likely primary voters—up 5 percentage points from February—followed by 7 percent for New Jersey Governor Chris Christie, 6 percent for Senator Ted Cruz of Texas, 5 percent for retired neurosurgeon Ben Carson, 4 percent for former Arkansas Governor Mike Huckabee, and 3 percent for former Hewlett-Packard CEO Carly Fiorina.

Scoring 1 percent were former Texas Governor Rick Perry, Louisiana Governor Bobby Jindal, Senator Lindsey Graham of South Carolina, former Senator Rick Santorum of Pennsylvania, and Ohio Governor John Kasich, none of whom have formally announced bids. 

Walker does best when first and second choices are combined, a positive sign for his prospects in the state. He's backed by 24 percent in that case, followed by 21 percent for Bush and Paul and 20 percent for Rubio.

“The Republican primary remains as wide open as ever, and there are no signs here that any candidate has a clear route to winning in New Hampshire,” Usher said.

Part of Paul's strength is his ability to attract independent voters, a key group especially in New Hampshire, where they can vote in partisan primaries. He's supported by 18 percent of independents who said they were likely to vote in the Republican primary, easily the most of anyone in the field. That means he's going to want to see the state's Democratic primary remain a lopsided affair, prompting independents to stick with the action on the Republican side and continue to support him.

Bush is relatively weak among independents. While drawing support from 15 percent of Republicans, he has the backing of just 6 percent of independents. That's a potential problem for Bush, especially if he runs poorly in the Iowa caucuses set for the week before New Hampshire's primary. A Quinnipiac University poll released last week showed Bush in 7th place in Iowa, so he might need a top finish in New Hampshire to rebound.

Fred McGarry, 69, a semi-retired engineer from Deerfield, N.H., said he's leaning toward Bush, although the moderate Republican said he wishes he had other choices.

“I'd be happier if his last name wasn't Bush,” McGarry said. “All the others are too far to the right for me and my guess is that some of them will play well in the strongly red states, but not get elected nationwide.”

The poll shows gender differences developing among likely Republican primary voters. Paul does twice as well among men as he does among women, while Rubio does slightly better with women than men. Walker also does slightly better among men. Bush performed equally well among both genders.

“Walker has got a lot of good credibility and his conservative vocabulary is excellent,” said John Van Uden, 79, a retired manager for a farm equipment company who lives in Bedford, N.H. “He knows what he's talking about from his experience as a governor.”

And New Hampshire voters aren't convinced that the next president will be named either Bush or Clinton. Asked to choose which of the two would be the next president, a third of New Hampshire's likely general-election voters said Clinton, 27 percent didn't venture a guess, 22 percent said someone else, and 18 percent said Bush.

Among Republican primary voters, 31 percent say they think another Bush will move into the White House in 2017, while 34 percent say someone else, 24 percent said they're not sure, and 10 percent said Clinton.

The poll included 500 general-election voters as well as over-samples to have 400 Republican primary voters and 400 Democratic primary voters. It has a margin of error of plus or minus 4.4 percentage points on general-election questions and plus or minus 4.9 percentage points on primary election questions.

More from the Bloomberg Politics/Saint Anselm New Hampshire Poll: Hillary Clinton Resilient in Nation’s First Primary

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