Florida Sen. Bill Nelson and Democratic leaders from his state plan to go forward with a proposal to hold a mail-in do-over of the state's discounted primary, arguing it's the most practical way to let voters have their say despite strong opposition from the state's Democratic House delegation.

Urging the campaigns and party leaders to consider the re-do, state party Chair Karen Thurman said in a memo containing a draft of the proposal that the idea would be to mail ballots to all registered Democrats and set up 50 regional voting offices to help "disadvantaged communities" participate.

State Senate Democratic leader Steve Geller said the party hopes to have a proposal firmed up by Thursday that would allow a 30-day review period and a vote by the party's executive committee April 12 on whether to hold the election. A likely deadline for mail-in ballots to be returned would be June 3.

Geller dismissed concerns that the state's House Democrats on Capitol Hill rejected the idea in a joint statement Tuesday night.

Nelson also told FOX News the delegation's position does not dash the effort to push for another election. He said he spoke with Democratic National Committee Chairman Howard Dean Wednesday and told him "people's ballots have to be counted."

The DNC stripped Florida and Michigan of their delegates for holding early primaries in violation of party rules. Florida officials and the campaigns of Barack Obama and Hillary Clinton have since been sparring over how to seat those delegations, if at all.

In the meantime, the party plans to begin raising an estimated $10 million to $12 million to pay for the do-over.

Nelson said in a statement that his first preference is to recognize the Jan. 29 primary, but that "party bosses" have been legally permitted to ignore that contest, forcing him to turn to a re-do.

"My next choice was a full-fledged re-vote run by the state," he said. "But officials said that would be too costly and insisted there wasn't time. In my view, at this late hour, mail-in balloting would be the most practical and fair way to let Florida voters have a full say in the selection of their Democratic nominee.

"If anyone has another way of accomplishing this, or of honoring the earlier results without splitting the convention, it needs to be put on the table -- and now, before it's too late. Time is short, and we need to make available for public comment a workable plan. The bottom line is: we all agree that the voters of Florida must be heard."

Nelson told FOX News he would push for security precautions, but steered clear of funding questions, which has been a major stumbling block.

Clinton again made the call Wednesday either to honor the results or hold do-over primaries.

"The results of these primaries were fair and they should be honored," she told the Hispanic Chamber of Commerce in Washington, D.C. "Over the last few weeks, there's been a lot of discussion over what we should do to make sure the voters in Florida and Michigan are counted. We have two options; honor the results or hold new primary elections. I don't see any other solutions that are fair and honor the commitment that 2.5 million voters made in the Democratic primaries in those two states."

The Obama campaign has said it will not accept the results based on the January contests, as Obama's name was not on the ballot in Michigan, and neither candidate campaigned in the Sunshine State.

Campaign manager David Plouffe said caucuses, however, were an option, as were new primaries, but cautioned the latter method would be expensive. He had "deep concerns" with a mail-in re-vote.

"It seems that the easiest solution here would be some kind of fair seating of the delegations that is not reflective of this contest in January, that allows these states to participate in Denver, but does not advantage Senator Clinton unfairly," Plouffe said.

It's unclear how this seating would be decided. But Plouffe said Clinton's push for the states is rooted in self interest, not a desire to fight disenfranchisement.

"We do not think the Clinton campaign's approach here is based on benevolence towards Florida and Michigan. It's based on increasingly desperate, self-serving stretching for whatever they think might help them secure the nomination," he said.

Obama told reporters Wednesday that his campaign is consulting with officials in Florida, Michigan and the DNC and he's confident something will be worked out.

"My bottom line is, I do want to make sure that the Florida and Michigan delegations have an opportunity to participate in the convention," he said. "And we want to figure out an equitable way to do that."

Michigan Democratic Party leaders were considering several options to get their delegates seated, including a mail-in vote or a state-run Democratic primary that would be held in May or June and paid for by Democratic donors. The latter plan would have to get Republican lawmakers' approval and faces numerous other hurdles.

Despite the possible problems, four Michigan Democratic leaders uncommitted to any candidate plan to run the idea past the Obama and Clinton campaigns Thursday during separate talks. DNC member Debbie Dingell, U.S. Rep. Carolyn Cheeks Kilpatrick, U.S. Sen. Carl Levin and Ron Gettelfinger are in that group.

FOX News' Trish Turner and Aaron Bruns and The Associated Press contributed to this report.