Special Elections in Context
That said, special elections to the House rarely mean anything. A very useful table compiled by Greg Giroux of CQ Politcs lays out all the House special elections of the past four decades. It's not hard to discern a pattern--the party out of power in the White House usually does pretty well, at least if the district is somewhat competitive.
But of all the party switches since 1968, only two seem to have indicated significant broader patterns: in 1969, when Wisconsin Democrat David Obey took the seat of Mel Laird, who had resigned to become Nixon's secretary of defense; and in 1993, when Republican Ron Lewis won a rural Kentucky district made vacant by the death of Democrat Bill Natcher. Obey previewed the type of young, politically talented Democrat who would ride anti-war fervor and support for ethics reform to the House in the 1970s, from districts long thought of as GOP bulwarks. And Lewis' win anticipated the 1994 GOP sweep of conservative Southern districts long represented by white Democrats.
Regardless of whether Murphy or Tedisco winds up prevailing, it's hard to see the New York race as a bellweather of anything significant.