Having now spent 6,000-odd words on the Florida special election, I should admit that smart analysts predicted the result with one number. Two-hundred thousand. If that many ballots showed up in FL-13, Democrats were hitting their turnout models and winning the race. If fewer, they were losing. There were about 180,000 votes cast in the race, and the Democrats lost.
It need not be this way. Recently, Jon Ward dug into the instantly forgotten story of how Virginia Democrats won two special elections for state Senate in Virginia. Both were for open seats, held by Democrats who'd become LG and AG in 2013.
Short version: As the elections loomed, incoming Gov. Terry McAuliffe hustled up $500,000 for the Democrats. That money was used hire "20 paid field organizers in each race," who worked off the "first-rate data analytics models" relied on by McAuliffe in his big-spending 2013 race. Democrats managed to pull out their vote in low-turnout January elections, one of them held during the nadir of the polar vortex freeze. They won.
But barely. (Sorry, I lied in the headline.) In 2011, Democrat Ralph Northam sailed to victory in his 6th District race—16,606 votes to 12,622 for his Republican opponent. In the 2014 special, Democrat Linwood Lewis won 10,203 votes, narrowly besting a Republican who won 10,192. The Democratic vote fell off much more steeply than the Republican vote.
In 2011, Democrat Mark Herring won the race in the 33rd District with 14,061 votes, beating a Republican who won 11,915. The race went far, far better for Democrats in 2014—Democrat Jennifer Wexton won by 15 points. But she only won 11,431 votes. A Republican and a party-switching spoiler won a combined 10,250 votes.
These are, as Ward says, the best recent test cases of how Democrats can bring enough of their base out to win in off-year elections. They did win. They did not solve the problem of Republicans turning out at a higher relative rate.