The Democratic National Committee wants both Michigan and Florida to have new elections so that their delegations can be seated at the Democratic convention. While the Republican Governor of Florida is open to the idea of a new primary, he doesn't think the state of Florida should pay for the primary. Howard Dean, Chair of the DNC, doesn't think that the DNC should foot the bill. One idea that is gaining traction is to have new primaries in each state by mail.
The process would be that every Democratic voter in each state would receive a ballot by mail and would then fill it out and return it to the Democratic Parties of their respective states. This would obviously be expensive, but probably not as expensive as paying for poll workers to cover polling places for 12 hours or more. Oregon votes by mail and reports few problems with the concept.
One interesting aspect to such a procedure would be that Republicans and independents wouldn't be able to participate, as they can in other primaries.