He pointed out the poll was conducted just days after Tennant announced she would run for Senate, while Capito has been campaigning since late last year.
"That's unbelievable, to have that close of a race this far out when one has the advantage of a whole year to campaign," he said. "I believe that it's a very exciting day today for Natalie Tennant."
Tennant's relative unpopularity among voters could be tied to West Virginia's low opinion of President Barack Obama.
Only 28 percent of poll respondents said they approved of Obama's job performance, while 67 percent said they disapproved.
Puccio said Obama's approval ratings are a definite negative for Tennant at this point, but said the connection will not harm her campaign in the long-run.
He said Republicans have tried a similar tactic, claiming a state Democrat candidate will become a "rubberstamp" for Obama, in races against Sen. Joe Manchin and Gov. Earl Ray Tomblin. The move was unsuccessful both times.
"I believe by the time we get to Election Day, that is old and abused. It hasn't worked two times in a row. Why would one believe it would work the third time?" he said.
Lou Ann Johnson, senior advisor for Tennant's campaign, said in an emailed statement Tuesday the candidate's polling numbers will improve once West Virginians learn more about her.
"Natalie Tennant has always put West Virginia first," she said. "In contrast, Congresswoman Capito puts Washington special interests ahead of West Virginia families, voting to allow bonuses for Wall Street bankers while collecting over $1.2 million in campaign contributions from Wall Street."
The Public Policy Polling survey included 1,110 West Virginia voters, including 600 usual Democratic primary voters and 348 usual Republican primary voters. The poll has an overall margin of error of 2.9 percent, 4 percent for Democrats and 5.3 percent for the GOP.
The study was conducted without any support from either political party.
These findings are quite different from the findings of the West Virginia Poll, conducted last month.
That phone survey found 45 percent of respondents said they would pick Capito, while 40 percent would choose Tennant.
The poll's margin of error made the race a dead heat.