Burke said she'd prefer to see a new arena paid for with private funds instead.
"I think (public financing) should be one of many options on the table," she told members of the Rotary Club of Milwaukee and the Milwaukee Press Club. "It frankly should be the last one."
The future of the BMO Harris Bradley Center, where the Milwaukee Bucks play, remains in doubt. Bucks owner Herb Kohl announced last month he was selling the team, and he and the buyers pledged a total of $200 million toward building a new arena. But that could still leave taxpayers on the hook for another $200 million or more.
Options include imposing a regional sales tax, such as the one that helped pay for the Brewers' Miller Park, or seeking money from private investors who would share in stadium revenue.
Burke is a former Trek Bicycle Corp. executive and state commerce secretary. She'll square off against three other Democrats - state Rep. Brett Hulsey, Marcia Mercedes Perkins and Hari Trivedi - in an Aug. 12 primary. The winner faces Republican Gov. Scott Walker on Nov. 4.
The Burke and Walker campaigns have said little about the stadium issue, mainly because the issue is in its early stages.
"Once we hear details of a plan from elected officials and civic leaders in Milwaukee, we will review and evaluate any role that might involve the state government," Walker's campaign said. "Any further comment right now would be premature."
Burke also took questions Tuesday on a number of other issues. For example:
- She said Walker's key failing has been an inability to create jobs. She said governors of neighboring states have been far more successful in that regard.
- Although she's never been a CEO or held an elected office, Burke said her experience as a Trek executive makes her qualified to be the CEO of Wisconsin. She said voters are sick of ineffective politicians and want to see a more businesslike approach to running the state.
- Democratic Gov. Jim Doyle, her boss when she led the state's commerce department, did a good job overall but just had the misfortune to be governor in 2008 when the entire country was plunged into a recession, she said.
- She declined to weigh in on whether the Menominee tribe should be allowed to open an $800 million off-reservation casino in Kenosha. She said the only studies done so far have been by groups with a stake in the outcome, and she'd rather see an independent study.
- She said she's not opposed to mining operations in northern Wisconsin as long as there are strict and well-enforced environmental regulations.