Gov. Scott Walker (R) is not safe in next month’s recall election, Wisconsin Democrats say.

Walker has been pulling ahead of Milwaukee Mayor Tom Barrett (D) in polls on the June 5 recall election sparked by the governor’s collective bargaining reforms. But internal polling from We Are Wisconsin, a labor-backed coalition supporting the recall, finds a dead heat.

Supporters of recalling Gov. Scott Walker celebrate in Madison, Wis., Jan. 17 after canvassers gathered about 1 million signatures. (Andy Manis/AP)

In a survey of 472 recall voters conducted by Greenberg Quinlan Rosner Research from May 19 to 21, Walker leads Barrett 50 to 47 — within the poll’s four-point margin of error. Barrett leads with independents, 50 percent to 44 percent.

We Are Wisconsin spokesman Kelly Steele argued that the polls showing Walker in the lead oversampled Republicans and that the “pre-mortems” are premature.

“[T]his race remains a dead heat, with Barrett solidifying and even building on his lead amongst Independents, and Democrats’ turnout operation in full gear as early voting and GOTV begin in earnest,” Steele said in a memo.

Three recent surveys gave Walker the advantage.

Public Policy Polling, a Democratic firm, showed Walker five points ahead in a survey conducted May 11-13. We Ask America, a Republican one, gave Walker a nine-point lead on the 13th. Marquette Law School showed the governor six points ahead in polling done May 9-12.

Barrett pollster Fred Yang told The Fix this week that internal campaign polling showed the race “neck and neck,” noting that the surveys being discussed in the media were conducted before the candidate’s recent ad offensive against Walker.