WASHINGTON -- A top Republican lawmaker in Wisconsin has suggested that GOP voters may cause mischief at the polls in May, when Democratic voters pick the candidate who will face Gov. Scott Walker (R) in the recall's general election in June.

Wisconsin has open primaries, allowing voters of any party to vote in any election. So Republicans are free to vote in Democratic primaries, and vice-versa.

There are currently four Democratic candidates competing in the May primary. Former Dane County executive Kathleen Falk and Milwaukee Mayor Tom Barrett are considered frontrunners, with state Sen. Kathleen Vinehout (D-Alma) and Secretary of State Doug La Follette also in the race.

On Monday, the Milwaukee Journal-Sentinel reported that Senate Republican Leader Scott Fitzgerald (R-Juneau) "said some Republicans may vote for Falk in the Democratic primary because polling shows she does not perform as well as Barrett in head-to-head matchups with GOP Gov. Scott Walker."

"There's nothing to keep the Republicans from messing around," Fitzgerald said, according to the newspaper.

Fitzgerald did not return a request for additional comment. Benjamin Sparks, communications director for the Wisconsin Republican Party, said the GOP sees no difference between Falk and Barrett.

"They're both more or less the same thing," Sparks told The Huffington Post. "They both are running on a platform of turning our state backward, and they both already lost statewide twice. So the only question is, which one will be next to lose a third time?"

Polls show Barrett and Falk running almost neck and neck.

In 2008, right-wing radio host Rush Limbaugh supported an effort called "Operation Chaos," encouraging Republicans to vote in Democratic primaries for Hillary Clinton to extend the Democratic primary process.

When asked whether Wisconsin Republicans were planning something similar for the recall, Sparks replied, "Uhh, no."

Scott Walker's campaign, asked for comment, replied, "Governor Walker is solely focused on sharing his pro-jobs, pro-growth message and his plans for using the foundation that has been laid to move Wisconsin forward."

Still, some Democrats and labor officials said they were troubled by Fitzgerald's remarks.

"I think obviously, regardless of your partisan background, it's just objectively offensive," said Jim Palmer, executive director of the Wisconsin Professional Police Association. "I think it's also a real sign that they're terrified, and the Republicans in Wisconsin will do anything they can -- even if it's causing mischief -- in order to maintain their power. I do also think, on a tangent somewhat, that it raises questions about Kathleen Falk's electability, and that's something that groups that haven't endorsed, like my own, need to evaluate."

Palmer's police association has not yet endorsed a candidate, although it has been sharply critical of the role of the American Federation of State County and Municipal Employees (AFSCME) in the recall. That union, along with several others, has endorsed Falk.

Falk's spokesman, Scot Ross, disputed the notion that Fitzgerald is going after Falk because she is the weaker of the two candidates.

"Kathleen's record and her vision for bringing Wisconsin together after Gov. Walker's failed policies, which tore Wisconsin apart, is why she's earned the support of every organization which has endorsed in the Democratic primary," Ross said in a statement. "This big tent of working men and women, environmentalists, women's rights advocates and young progressives is what Wisconsin will need to defeat Gov. Walker and his unprecedented millions of dollars from out-of-state billionaires and millionaires. Sen. Fitzgerald is going after Kathleen because he knows how hard she worked around Wisconsin during the Senate recalls and he knows she is best positioned to defeat Gov. Walker."

In addition to the four Democrats in the primary, there is one Republican woman running as a fake Democrat. There are a total of six fake Democrats fielded by the Wisconsin GOP running in the recall races for governor, lieutenant governor and state Senate.

The Republican Party has said that the "recall protest candidates" are simply meant to guarantee a clear primary date and ensure that no Republican will face a general election in May, when Democrats are expected to turn out in large numbers for the gubernatorial recall primary.

The primaries are scheduled for May 8 and the general elections are set for June 5 -- unless there are no primaries for a particular post, in which case the general election for that post would take place on May 8.