Florida, the state that cost the Democrats the presidency in 2000, once again may be throwing the party's hopes of winning the White House into turmoil.

The impasse over Florida's delegation to the Democratic National Convention deepened Thursday, as the state's Democratic House delegation again gave the thumbs-down to a proposal to hold a re-do of the state's nullified January primary.

"After reviewing the Party's proposal and individually discussing this idea with state and local leaders and elections experts, we do not believe that this is a realistic option at this time and remain opposed to a mail-in ballot election or any new primary election in Florida of any kind," the delegation said in a statement, adding it was still "committed" to finding a way to seat the delegation.

Florida Democratic Party Chairwoman Karen Thurman made the pitch for a combined mail-in/in-person do-over election, casting it as the only viable way to resolve the dispute. But she acknowledged early on the plan has only a slim chance of passing.

"The stark reality is that all Democrats lose if this is not resolved immediately," Thurman wrote in a memo sent late Wednesday to Hillary Clinton, Barack Obama and the national party and the Florida congressional delegation.

She asked for all the parties to return comments by the end of business Friday. Thurman will review comments and make a decision by Monday on whether to proceed, but she said based on what she's already heard, it's unlikely to happen.

Click here to read the full letter and draft Florida mail-in ballot plan (.pdf).

The Democratic National Committee stripped Florida and Michigan of their delegates to the national convention when the two states decided to hold their primaries earlier than DNC rules allowed.

Clinton won the Florida primary handily, although none of the Democratic candidates campaigned in the state and none of them aired any commercials targeted to its residents. Clinton also won the Michigan primary, although she was the only top-tier Democratic candidate whose name appeared on the ballot there. "Undecided" was the runner-up in Michigan.

"Unfortunately," Thurman wrote, referring to Florida, "it is becoming increasingly clear that there is no possibility the presidential campaigns and the DNC will agree to seat the delegation as is. Some have suggested that to resolve this issue Florida's delegation be split evenly between the candidates, and potentially restore the superdelegates votes. However, the DNC has informed the party that this is not an option under the rules."

The only remaining solution is a do-over primary. But Florida cannot conduct a conventional vote for several reasons, so Thurman said a mail-in ballot is the only option.

Officials have shared with FOX News a number of details about their efforts to work this out, including the ballot's appearance; the prepayment for the postal charge; outreach to potentially unaware groups such as low-income or nursing home residents; and likely participation levels, which they put at more than 2 million.

The plan would work mostly through mail, but 50 temporary offices would be scattered around the state "to ensure that disadvantaged communities have the ability to vote." Voters could cast provisional ballots at the temporary offices if there's a problem.

A draft of the plan circulated by Thurman calls for 30 days of comment before it is finalized. Voting would take place on June 3.

On Wednesday, nine House Democrats first voiced their opposition to a mail-in ballot because Florida has not tried it before, although the system has worked in Oregon and Washington state.

Some opponents to the plan argue that many Floridians head north in June, when the balloting would take place. Others say low-income voters may have "inconsistent addresses" because they are more likely to move around and could be hard to reach.

One thing is clear, said Florida Rep. Kendrick Meek: Finding a solution to the dilemma "has gone from moving at a snail's pace to warp speed."

If Democrats are unable to hold a second ballot, some fear, the outcome of Florida's Jan. 29 primary will be completely ignored.

"No action is truly a solution if it leaves Florida voters feeling that they were excluded from the most exciting nominating contest in history," Thurman wrote.

FOX News' Jim Angle and The Associated Press contributed to this report.