Updated

Supporters of a push to oust Wisconsin Gov. Scott Walker from office are prepared to declare victory in their effort to force the Republican into a recall election. But a problem looms for Democrats: They still don't know who would run against him.

Recall organizers say they have gathered far more than the 540,208 signatures required to force the election against both Walker and GOP Lt. Gov. Rebecca Kleefisch, and will submit their petitions Tuesday.

Walker has meanwhile dominated the state's airwaves with ads defending his agenda, including the law enacted last year that ended nearly all collective bargaining rights for most public workers and spurred the recall effort in the first place.

He's also crisscrossed the country raising millions of dollars, taking full advantage of both the conservative rock star persona built as he put Wisconsin at the center of the national labor rights debate and a quirk in state law allowing those targeted for recall to ignore normal contribution limits until an election date is set.

Walker reported in mid-December that he'd already raised $5.1 million, with about half of that coming from out of state. He received $250,000 alone from Bob Perry, the Texas conservative who was one of the main financial backers behind the Swift Boat Veterans ads that attacked Sen. John Kerry during the 2004 presidential campaign.

Democrats and union leaders insist they're not concerned about not having someone actively running against Walker and trying to match his fundraising. In fact, they say it was part of their strategy.

"It forced Walker and his minions to run on their record and issues rather than to run against an announced Democratic candidate," said Marty Beil, president of the Wisconsin State Employees Union, the largest union of state workers. "That was part of the rationale through the whole recall petition collection process."

Democrats and union leaders said they also never anticipated competing with Walker on fundraising. Beil said the key for recall supporters will be to maintain the enthusiasm that fueled recall signature collection for the past two months.

"And we win with some resources, but we don't see matching him for dollar by dollar," Beil added.

Walker's campaign spokeswoman Ciara Matthews said in a statement that the governor's record will "stand in stark contrast to whoever the eventual Democratic nominee is." She defended Walker's record from last year, noting he balanced the state's $3.6 billion shortfall without massive layoffs of state employees.

Democrats have framed Walker's budget-balancing tactics as an attack on labor unions, one of their key constituencies. Thousands of demonstrators staged non-stop protests at the Capitol for three weeks and the Senate's 14 minority Democrats even fled the state in a futile attempt to block the collective bargaining plan that Walker signed into law last March.

The Democratic field of would-be challengers to Walker is expected take shape once the Government Accountability Board certifies that petition circulators have gathered enough signatures. Beil said he expected it be clear by the end of the month, while state Democratic Party Chairman Mike Tate said he didn't expect a set field before March.

"I don't see any need for a candidate to dip their toe in the water until they absolutely feel it is necessary to do so," Tate said. "We have a blessing of riches in the Democratic Party. We have several people who would make wonderful governors."

Numerous prominent Democrats have said they're considering a run but the two highest profile ones — former Sen. Russ Feingold and retiring Sen. Herb Kohl — have repeatedly said they aren't interested.

Moderate Democrat state Sen. Tim Cullen has said he intends to take on Walker but has not made a formal announcement or been actively campaigning. He said he expects and welcomes a Democratic primary, which likely would be held in May, although the timing will be unclear until possible delays related to the signature verification process and any legal challenges are resolved.

"If there's not a primary, then who's actually deciding this?" Cullen said.

Walker and his allies say organized labor will decide the Democratic candidate. Public workers and their unions have been a driving force behind the recall, helping provide the manpower needed to circulate petitions.

Union leaders have made some of their preferences known. They've been clear in their distaste of a potential candidacy by Milwaukee Mayor Tom Barrett, who lost to Walker by 5 percentage points in 2010. Barrett has angered some unions with cuts he made to the city budget and his support of a plan a couple years ago that would have given him control of the troubled Milwaukee Public Schools.

Beil and Mary Bell, the head of the statewide teachers union, met with Barrett in December and unsuccessfully tried to dissuade him from running, based on an email Bell sent to other union leaders that was first reported by the Milwaukee Journal Sentinel.

Bell confirmed the meeting and email to The Associated Press but declined to comment in more detail about Barrett or who the union is supporting. Beil also has been outspoken in his opposition to Barrett but won't say who the union supports yet.

Barrett has announced that he's seeking re-election as Milwaukee mayor, which will be decided on April 3. But he's repeatedly dodged questions about another run against Walker, refusing to rule it out or commit to it.

"The candidate has to be a champion of these thousands of people who have said we need a change," Beil said. "The candidate has to be a champion, it can't be the same old message."

One potential candidate organized labor does like is Kathleen Falk, a retired Dane County executive who said she is considering running. Falk, who previously ran unsuccessfully for governor and state attorney general, has been traveling the state speaking out in support of the recall.

Other potential Democratic candidates include former U.S. Rep. Dave Obey, current U.S. Rep. Ron Kind, state Sen. Jon Erpenbach and state Rep. Peter Barca.