A new Daily Kos-sponsored Public Policy Polling poll in Wisconsin shows that neither of the main Democratic challengers to Gov. Scott Walker are leading him — Walker holds a 5-point lead over Milwaukee Mayor Tom Barrett and a 7-point lead over labor-backed former Dane County Executive Kathleen Falk.

In the primary, Barrett leads Falk by a 38 to 24 spread — a 14-pt margin. This is a smaller lead than in the last PPP poll, but still substantial, and it could spell trouble for the unions that are the biggest motor in the fight to remove Walker.

The Democratic primary to decide Walker's opponent will be held on May 8, and the race has turned increasingly nasty, raising concerns that the food fight will hamper the Democrats when the recall rolls around in June.

Organized labor is mostly behind Falk, as the two largest public sector unions in Wisconsin— WEAC and AFSCME — have supported her, as well as a number of other major unions. But even in a race that hinges on labor issues, that doesn't seem to be enough to move the numbers. Barrett has the advantage of having run a statewide race before, plus wider name recognition as the mayor of the state's largest city. Attacks from his left and from Walker's camp have dinged him, but won't make a real impact with voters in time for the election at this rate.

Still, neither challenger is touching Walker, a possible consequence of the infighting on the Democratic side. Barrett's communications director Phil Walzak told BuzzFeed that "the fact they have just a five point lead despite that huge spending advantage shows how vulnerable they are." He noted that the Walker side has been spending millions on television for months.

The Falk side countered with a press release with the subject line, "Falk Cuts Barrett Lead in Half." Barrett was leading Falk by a 45-18 margin in the last PPP poll in February, leading spokesman Scot Ross to write that "Momentum is with Kathleen Falk."

"The only thing that matters is the versus-Walker numbers," said one Wisconsin labor operative. "The only thing people care about is the ability to beat Walker."

Barrett's "claim he's better versus Walker isn't borne out in polling over time," the operative said.

Wisconsin for Falk, the pro-Falk independent expenditures group, sent out an email to supporters making a similar argument: "Did you catch the news last week that Kathleen Falk and Tom Barrett are equally competitive against Scott Walker in a general election matchup?"

It continues, "Mr. Barrett and his allies are going to great lengths to advance the idea that he is the best candidate to defeat Scott Walker in a general election, but they offer no evidence to support their claim."

Walker's spokeswoman Ciara Matthews struck a confident note in an email to BuzzFeed, saying "We are confident that because the positive effects of his reforms continue to create more jobs and keep more money in the pockets of taxpayers, voters will reaffirm the decision they made a year ago."