The survey, conducted by Democratic firm Public Policy Polling, gives Paul 20 percent support to Christie's 19 percent among Republican primary voters.

The poll has bad news for Sen. Marco RubioMarco Antonio RubioOvernight Cybersecurity: What we learned from Carter Page's House Intel testimony | House to mark up foreign intel reform law | FBI can't access Texas shooter's phone | Sessions to testify at hearing amid Russia scrutiny Cornyn: Senate GOP tax plan to be released Thursday This week: GOP seeks to advance tax overhaul MORE (R-Fla.) who has fallen 18 percentage points since April. He now registers just 7 percent support in the primary.

In an imagined general election, Christie narrows Clinton's margin in the state to just four points, taking 39 percent support to her 43 percent. Against Paul, she takes 51 percent to his 41 percent support. 

The former secretary of state is the leading contender for the Democratic nomination in the poll, as she has been in every survey of the likely Democratic presidential field. She draws the support of 57 percent of Democratic primary voters, far ahead of Vice President Joe BidenJoseph (Joe) Robinette BidenThe Hill's 12:30 Report Pence talks regularly to Biden, Cheney: report Biden moving toward 2020 presidential run: report MORE's 12 percent support and the 11 percent who favor Sen. Elizabeth WarrenElizabeth Ann WarrenBipartisan group of lawmakers aim to reform US sugar program Schumer: Dems want DACA fix in government spending bill The Hill interview — DNC chief: I came here to win elections MORE (D-Mass.). No other contender breaks 10 percent.

Even so, this is a slight decrease for Clinton from the last PPP poll, in April, when she took 68 percent support. In the interim, support for Warren has edged up from 5 to 11 percent.

In a general election match-up, Clinton holds leads against other high-profile Republicans ranging from 8 points over New Hampshire Sen. Kelly AyotteKelly Ann AyotteTrump voter fraud panel member fights back against critics Dems plan to make gun control an issue in Nevada Stale, misguided, divisive: minimum wage can't win elections MORE to 12 points over Texas Sen. Ted CruzRafael (Ted) Edward CruzOvernight Finance: GOP criticism of tax bill grows, but few no votes | Highlights from day two of markup | House votes to overturn joint-employer rule | Senate panel approves North Korean banking sanctions GOP criticism of tax bill grows, but few ready to vote against it Anti-gay marriage county clerk Kim Davis to seek reelection in Kentucky MORE.

That's good news for Christie. If he runs, observers believe he will argue that he would be the most electable candidate in a general election. To buttress his case, he's working to win his upcoming gubernatorial reelection fight in a blue state by a significant margin.

If both he and Paul enter the race, the battle in the Granite State primary will be fierce.

Paul's father, former Rep. Ron Paul (R-Texas), had a strong following in New Hampshire, and the state has a long-established libertarian streak. But Christie is well-known to New Englanders in part because of his outspoken advocacy for Hurricane Sandy victims, which also hit parts of New Hampshire.

Over Sept. 13-16, PPP surveyed 455 usual Democratic primary voters and 491 usual Republican primary voters. The Democratic portion of the poll has a plus or minus 4.6 percentage point margin of error and the Republican portion has a plus or minus 4.4 percentage point margin of error. The overall poll has a 3 percentage point margin of error.