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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 Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Trump bets base will stick with him on immigration 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 BidenBiden slams Trump over golf gif hitting Clinton Overnight Tech: Equifax hit by earlier undisclosed hack | Facebook takes heat over Russian ads | Alt-right Twitter rival may lose domain Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE's 12 percent support and the 11 percent who favor Sen. Elizabeth WarrenElizabeth Ann WarrenSenate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Trump bets base will stick with him on immigration Dems call for action against Cassidy-Graham ObamaCare repeal 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 AyotteStale, misguided, divisive: minimum wage can't win elections Trump voter fraud commission sets first meeting outside DC RNC chair warns: Republicans who refused to back Trump offer 'cautionary tale' MORE to 12 points over Texas Sen. Ted CruzRafael (Ted) Edward CruzSenate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea GOP state lawmakers meet to plan possible constitutional convention 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.