The New York State Board of Elections has a lot of data (.pdf) out on absentee ballots in the special election in that state's 20th Congressional District, which will be vital in breaking the virtual tie between Scott Murphy and Jim Tedisco.
One thing that seems fairly clear is that there tend to be a relatively higher proportion of absentee ballots returned in counties where Murphy performed well on election night. For example, Columbia County, where Murphy won 56.3 percent of the of the vote last week, accounted for 9.8 percent of ballots on election night, but accounts for 15.3 percent of absentees. Conversely, Saratoga County, which is a Tedisco stronghold, represented 36 percent of ballots on election night but only 27.2 percent of absentees:
If I simply apportion the absentee ballots based on the distribution of the election day vote in each county, I show Murphy gaining a net of 173 ballots during the absentee counting phase. In addition, as Michael Barone has noted, although a plurality of the absentee ballot returns are Republican, they are somewhat less Republican than registration in the district as a whole.
The absentee ballot counting process begins tomorrow. Murphy presently appears to lead by 83 votes, although the numbers have been fluctuating somewhat wildly. While nothing's for sure yet, things are starting to look a bit difficult for Tedisco; he may need some good news from one of the two counties that have yet to finish re-canvassing their results, or a lot of help from military absentee ballots (of which only about 200 were returned).
(n.b. See also Campaign Diaries, which has a similar analysis)