One potential candidate is Milwaukee Mayor Tom Barrett, who was the Democratic nominee against Walker in 2010, losing by a 52%-47% margin in that heavily Republican year. Barrett has been moving toward another run -- but at the same time, officials in the public employee unions have been very openly opposing him, due to various disputes involving the city's budget and public school system.
However, a survey released this week by Public Policy Polling (D) showed that Barrett would start out as the frontrunner in a Democratic primary, but that the race could also still be fairly wide open.
During an appearance Tuesday evening on Al Sharpton's MSNBC show, Barrett was asked whether he will run again in the recall.
"Well, Reverend Sharpton, right now I'm running for re-election as mayor, and that's what I'm concentrating on," said Barrett. "And today's a day to celebrate -- but not just celebrate, prepare for the future. So there's going to be plenty of time, and I guarantee you there will be a strong, if not more than one, strong Democratic candidate for this office. But right now, I don't think that's the time to speculate as to who the candidate should be.
"What we have to do is, we have to set our focus and our sights on making sure that we withstand any legal challenges to these signatures -- because again, they're going to try to color the state's perception of what has been an extraordinary, historic effort in this state."
In addition, former Dane County Executive Kathleen Falk, who like Barrett previously ran in the 2002 primary for governor, and in 2006 lost very narrowly as the Democratic nominee for state attorney general, released this statement on Tuesday, after the signature numbers were announced:
The people of Wisconsin have spoken loudly, an incredible one million strong, demanding the recall of a governor whose failed policies and extreme agenda have torn our state apart. Now, there should be no delaying tactics and legal tricks by Governor Walker and his allies to try to postpone the election. Let's go.
Other Democrats are also looking at the race, including those currently in the state legislature. State Sen. Tim Cullen took the first step among potential Democratic candidates in December, telling the Janesville Gazette that he would run in a primary: "I think I have credentials to be governor. I have executive experience in the public and private sectors. I believe I offer a resume where people can come forward and trust me as their governor."
Cullen did not immediately return TPM's request for comment on Tuesday.
Also among the legislators eyeing the race is Assembly Minority Leader Peter Barca, who led his caucus's opposition to Walker's legislation in a series of round-the-clock floor debates.
"Well, you know at this point, I really have not ruled it in or ruled it out," Barca told TPM. "It's still an open question, something I'll be analyzing very closely as we move forward over the course of the next eight weeks while the GAB is certifying the sigs and calling for an election."
Barca also added: "I guess I'm analyzing, versus the other candidates who are running, who would be in the strongest position to win the race, and govern effectively."
Would a primary put the party in a weaker position than if there were a consensus candidate, TPM asked?
"Well you know, it's always difficult to know. Primaries sometimes are useful if the strongest candidate can emerge. Primaries are sometimes very helpful. Obviously the degree to which people remain focused on why we feel need a change in the governor's seat, and focused on the Governor, versus attacking each other -- that would certainly be a plus."
Also considering the race is state Sen. Jon Erpenbach, who was among the Democratic state senators who fled the state last February in an attempt to block the bill.
"I'm taking a look at it," said Erpenbach. "What I'm doing more is responding to tweets and Facebook messages and e-mails of people wanting me to think about. when I go around the state people want to know if I'd do it, and if I did they would support me for it."
Erpenbach discussed his commitment to collective bargaining as the "cornerstone" of the recall campaign, as well as other issues such as education and jobs. He also gave a very open analysis of his profile as a candidate, pointing to how he has attracted the support of many grassroots Democrats after having a leading media role during last year's walkout -- but at the same time, some independent voters might not have agreed with the tactic and his major role in it, even though they nevertheless agreed on the core issues.
"It's the situation for me personally, I'm all about defeating Scott Walker, and if I'm the best candidate to do that great, and if I'm not the best candidate and someone else is, then that's great too. So that's where I am right now in the thought process."
Erpenbach also said: "A primary might be a good thing. The ability for everybody to have a say, who's working on the recall, for everybody to have their opinion, I think would be a good thing."