(CNN) -- Florida Democrats want a new primary vote, and state party officials have a proposal for recouping the 210 delegates the Sunshine State lost when it moved its primary ahead of the approved time frame.
State Democratic officials knew voters' ballots wouldn't count when they were cast January 29.
The party is proposing a combination mail-in and in-person election to be held June 3. Fundraising and public comment would begin immediately.
"The plan would be inclusive of all Democratic voters," according to a memo accompanying the draft plan that was sent Wednesday night to party leaders, including Democratic National Committee Chairman Howard Dean and Sens. Barack Obama and Hillary Clinton, the party's candidates for the presidential nomination.
Any plan would need the blessings of the DNC and the Clinton and Obama campaigns.
"We really believe that all Floridians deserve to be heard," said state party Chairwoman Karen Thurman, but "if this is not what the people of Florida and our presidential candidates want, then we're not going to do it."
The proposal could prove problematic because Florida law bans the state from conducting elections by mail.
State party officials could outsource the election operations to a third party, but the company would need voters' signatures to verify the voter rolls. In Florida, it is illegal to sell voters' signatures.
Dean said Thursday he had not yet seen the proposal, but acknowledged that it isn't perfect.
"Of course there are going to be problems," he said, explaining that is why state party officials are floating a proposal -- to get the kinks out. 
Watch how a mail-in vote could affect the race »
The cost for the proposed elections would be between $10 million and $12 million, according to the state party memo.
The DNC stripped Florida of its delegates when the state moved its primary to January 29, ahead of the DNC-approved time frame. The DNC also stripped Michigan of its delegates; voters there cast ballots January 15.
Florida's Democrats knew when they cast ballots in January that their votes would not count because the primary date violated party rules. Neither candidate campaigned there, though Clinton held a few permitted fundraisers.
Clinton handily won Florida, winning not only most of the counties but also every county in the lower three-quarters of the state. She took 50 percent of the vote to Obama's 33 percent. Former North Carolina Sen. John Edwards, who has since dropped out of the race, snared 14 percent of the vote.
As the race for the Democratic presidential nomination nears its finish -- 42 states have voted -- Obama leads Clinton in the delegate count, 1,611 to 1,480, according to CNN estimates. Clinton has the slight edge among superdelegates, 237 to 207.
If Florida were permitted to vote again, its 210 delegates could prove integral in determining the party's choice to challenge the presumed GOP candidate, Sen. John McCain of Arizona.
A Democratic candidate needs 2,025 to secure the party nomination.
In Washington on Wednesday, Clinton said the results in Florida and Michigan were fair and should be counted. However, she would be open to new elections if the DNC won't honor the January results.
"There are two options: Honor the results or hold new primary elections," she said. "If you're a voter from Florida or Michigan, you know that we should count your votes."
Obama said Thursday that the notion of counting the January results "just defies logic" because he didn't campaign in either state and his name wasn't on the ballot in Michigan.
"I think you could ask my 6-year-old whether that was fair and she would probably be able to say, 'No, that isn't,' " he said.
As for the Florida proposal, Obama reiterated his concerns -- chiefly about security -- regarding a mail-in vote, but said his campaign is "not going to make the final decision on it and I'll abide by whatever rules the DNC lays out."
Dean said the DNC would work to find an option amenable to both candidates, "something that puts the vote back in the hands of the people of Florida and Michigan, but that is not easy to do."
Florida's congressional Democrats tried Tuesday to hammer out a way to count the state's voters in the nominating process. Mail-in and do-overs were proposed, but lawmakers failed to reach a consensus.
Sen. Bill Nelson, D-Florida, has been vocal in his support of conducting a revote "principally by mail," but Rep. Debbie Wasserman Schultz, D-Florida, has said her House delegation "is opposed to a mail-in campaign or any redo of any kind."
According to a draft timeline included in the Wednesday memo, fundraising and public comment on the proposal would begin immediately and last through April 12.
The state's executive committee would discuss the proposal before sending it to the DNC for approval April 14. Mail-in vote packets would be sent to voters in mid-May, two weeks before the June 3 primary.
Those casting ballots in person would have to visit one of the 50 election offices set up across the state, rather than the thousands of polling stations that typically handle presidential elections in Florida.
The offices would be set up "to ensure disadvantaged communities have the ability to vote," the party memo said. E-mail to a friend 
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