That's what TNR's John Judis thinks, and he concludes the tie is good news for the President.

Special elections in the first year of a new president are important because the parties turn them into national referenda. And this election was no exception. Obama and Vice President Joe Biden campaigned for Murphy in the closing weeks; Murphy, who was relatively unknown in the district, based his campaign largely on his support for and Tedesco's opposition to Obama's stimulus plan...

Murphy's election night edge doesn't suggest that the Democrats will romp in 2010. Too many things can happen in the meantime. But if Murphy had lost by a significant margin--say 56 to 44 percent--it would have shown that within a district that Obama carried in 2008, there was a significant undercurrent of discontent with his presidency and his policies. That would have emboldened Obama's opponents.

So, is it?

Answer: not necessarily.

In an article written in 1999 for Legislative Studies Quarterly, Keith Gaddie, Charles Bullock, and Scott Buchanan ask "What is so special about special elections?"

They look at special elections over a 26 year period, 1973 to 1997. They try to predict the outcome of special elections based on six distinct factors:

(a) Presidential job approval
(b) Whether the candidates held previous elective office
(c) How much money each candidate spent
(d) The racial and ethnic composition of the electorate
(e) The normal partisan vote in the district (i.e. the average GOP presidential vote in the last two cycles)
(f) Time

They run the same model for special elections and open seat, regularly scheduled elections - and they find that presidential job approval is not a statistically significant factor in special election outcomes. Generally, they conclude:

In the context of congressional elections in general, special elections are as vulnerable to the constituency characteristics and candidate-specific attributes that structure other open-seat outcomes. In that respect, then, special-election outcomes that change partisan control can be viewed as the product of normal electoral circumstances and not referenda on the administration.

This conclusion is similar to the one that Frank Feigert and Pippa Norris draw in their 1990 study of special elections (also in LSQ) in the U.S., Britain, Canada, and Australia. Like Gaddie et al., they infer that candidate-specific factors are more in play.

Now, this doesn't mean we can draw a firm and final conclusion. There are reasons why presidential job approval might not have been a factor in the Gaddie/Bullock/Buchanan model but actually mattered in NY-20. The insignificance of presidential job approval in their model might be a statistical blip. Additionally, special elections have not received much scholarly study - so our conclusions must remain tentative. Also, the nature of these special elections might have changed since 1997, making them more "national" and a kind of referendum on the President. This election in particular might have been a referendum because of the salience of national news at this point (the bank bailout, the recession, etc).

However, these findings should give us pause before we go along with Judis's conclusion. There is evidence that special elections, while generally mimicking the factors that influence open seat contests, are not referenda on the President.