The Government Accountability Board on Tuesday gave tentative approval to Hulsey's nomination papers, meaning he appears to have the 2,000 signatures needed to get on the ballot. He had 131 over the minimum.
The board is meeting June 10 to certify candidates for the Aug. 12 primary. Objections can be filed through Thursday.
Another lesser-known Democrat, Marcia Mercedes Perkins, does not appear to have enough signatures. The board says her petitions have been denied.
Burke turned in 3,778 valid signatures while Republican Gov. Scott Walker had 3,825.
Libertarian and Peoples Party candidates also have gotten tentative approval to be on the ballot.