Rasmussen Reports found that each holds 45 percent support, though Walker has an edge in his favorable rating, 49 percent to Burke's 40 percent.
He also wins on economic questions, though more Wisconsin voters, by a 45 percent to 40 percent margin, trust Burke more on social issues.
Walker won men, older and married voters, and those who earn $50,000 or more. Burke won women, younger voters and minorities.
The poll of 500 likely voters conducted March 10-11 suggests that Burke's ad, in which she wrongly said that unemployment has gone up under Walker, has had some impact. A previous Milwaukee Journal Sentinel poll from January had Walker up over Burke, 47 percent to 41 percent.
Helping Burke, a Madison, Wis., school board member and daughter of Trek Bicycle founder Richard Burke, could be President Obama's better-than-average approval rating in Wisconsin at 53 percent. Some 50 percent approved of Walker in the Rasmussen poll.
Walker was elected in 2010 with 52 percent of the vote and won a recall election in 2012 with 53 percent support.
Walker has been an embattled governor ever since he took on state employee unions and won. That, coupled with his recall victory and conservative approach in the liberal state, has fueled speculation that he would run for the GOP presidential nomination in 2016.Paul Bedard, the Washington Examiner's "Washington Secrets" columnist, can be contacted at email@example.com.