The Marquette law school poll released Monday says 47 percent of registered voters would vote for Walker and 41 percent support Burke. The margin of error is plus or minus 3.5 percentage points.
A Marquette poll conducted in October showed Walker with a smaller edge over Burke, 47 percent to 45 percent.
Pollster Charles Franklin says the numbers suggest people are still making up their minds about Burke, a former executive with Trek Bicycle Corp. He says it's interesting that Walker's number didn't go up, considering that he has a 51 percent approval rating.
The poll of 802 registered voters was conducted from Jan. 20 through Thursday, with about 700 interviews conducted before the governor's State of the State address last week.