In a poll of registered voters, Barrett led Walker 47 percent to 46 percent, a lead that is reversed when polling only likely voters, the results released Wednesday revealed.
It's "just about as close to a tie as you can possibly get," said the poll's director, visiting Marquette political science Professor Charles Franklin.
Walker fared better against former Dane County Executive Kathleen Falk, beating her 49 percent to 42 percent. He has an even greater lead of 49 percent to 40 percent in head-to-head match-ups against Secretary of State Doug La Follette and state Sen. Kathleen Vinehout.
"We're obviously the strong, clear choice to take on Walker," Barrett spokesman Phil Walzak told the Milwaukee Journal-Sentinel. "People don't think the Walker way is working."
Heading into Tuesday's Democratic primary, Barrett led with 38 percent of those polled supporting him. Falk had 21 percent, Follette had 8 percent and Vinehout had 6 percent. Sixteen percent were undecided.
Walker will face protest candidate Arthur Kohl-Riggs in the GOP primary Tuesday.
The recall effort against Walker, a Republican, began soon after he pushed through the GOP-controlled Legislature a law last year effectively ending collective bargaining rights for most state workers. The general recall election will be June 5.
The margins of error for the polling questions ranged from 3.8 to 4.7 percentage points.