A few thousand votes?
Understand ANY candidate on the Rep or Dem ticket has a 50/50 chance and I do not care who is picked to represent. The fact is that the Dems cannot breach 49% of the vote, and haven't been able to since Carter barely managed it in his first election after Watergate and 'Nam.
Chances for success among Democrats are..
1) A poor representative for Reps.
2) Southern "perceived" conservative or moderate Democrat.
Reagan won two Majority votes, Bush came close in first, won the majority in second. Bush 41 won the first on Reagan's coattails, lost the second because he was perceived to have betrayed the base. Dole was uninspiring as a candidate. To cancel out the first means to victory for Dems is to find someone the conservative base can at least like. Not always in agreement with, but like.
The second is entirely up to the Dems. If Republicans find a candidate they can support in reasonable good conscience, the Democrat's best hopes are to nominate Warner because he fits the second criteria. If we don't find someone tolerable, they can nominate anyone they want and have a chance to win with less then 50% of the vote.
Don't forget Carter ran as a populist "smaller, lest pretention Govt?" type while Bill Clinton ran as a "new kind of Democrat and won largely because of the Ross Perot "fix the defecit" rebellion among Conservatives. Since the 60's radicals took over the Democrat party in the early 1970s, the Democrats have NEVER won on their chore views