MILWAUKEE (Reuters) - Opponents of Wisconsin Republican Governor Scott Walker said on Thursday they have collected 94 percent of the signatures necessary to force him into a recall election next year.

The group United Wisconsin, which opposes restrictions on public sector unions signed into law by Walker earlier this year, said it now hopes to gather 720,277 signatures by January 17 to force the recall election.

The group said it had already collected 507,533 of the 540,208 signatures required to force the vote.

Their goal of more than 700,000 signatures would represent 33 percent of the 2010 general election turnout and nearly 21 percent of all Wisconsin registered voters.

The few opinion polls on a Walker recall taken so far suggest a very close vote with the state polarized between outraged Democrats and Republicans who feel he did the right thing to improve the state's finances.

In response to the announcement by petition organizers, Republicans said they were confident Walker would survive any recall effort.

"Wisconsin voters ... have zero desire to go back to the failed policies of the past," said Ben Sparks, spokesman for the Wisconsin Republican Party.

Walker's campaign announced that it had raised more than $5.1 million from 46,976 individual donors. "We have seen an outpouring of support for the governor and the steps he has taken during his first year in office to lay the foundation for a more successful Wisconsin," said Walker's communications director Ciara Matthews.

Walker, elected in 2010 with 52 percent of the vote, and a Republican-controlled legislature, passed a raft of controversial measures this year including strict limits on the power of public sector unions.

The anti-union measure triggered a fierce political backlash from Democrats and union supporters.

Republicans also passed a voter ID law opposed by Democrats and concealed carry gun legislation

Six Republican state senators faced recall last summer over their vote in favor of the union restrictions and two were recalled.

Organizers of the current effort to recall Walker have to submit the signatures to the state's Government Accountability Board, which will then determine their validity.

GAB officials said this week they may need more than the 31 days allowed by law to finish the process.

Once the petitions are verified a date would be set for the election and Democrats would pick a candidate to oppose Walker.

Walker's campaign on Thursday filed a lawsuit saying the process for reviewing recall petitions is illegal because it puts the onus on targeted politicians to find duplicate signatures.

In addition to Walker, as many as 17 state senators -- 11 Republicans and six Democrats -- and the state's Republican lieutenant governor could face recall elections next year.

State rules allow such special votes if the lawmaker has been in office for at least one year and has not already faced recall.

Republicans hold a comfortable majority in the State House of Representatives but the political balance of the state Senate is 17 Republicans and 16 Democrats.

(Writing and additional reporting by James B. Kelleher; Editing by Greg McCune)

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