The candidates battling in the 20th Congressional District in the mostly rural north of the state are almost neck and neck, with Democrat Scott Murphy a fraction ahead of Republican Jim Tedisco, according to one poll.
The result will make no difference to the balance of power in the House of Representatives in Washington, where Democrats enjoy a big majority.
But the race is the focus of national attention as the first voter verdict on Obama's attempts to pull the country out of financial crisis and recession.
"It's the first early public referendum on the Obama presidency," said Richard Himelfarb, politics professor at Hofstra University.
The most contentious debate in the contest has been over Obama's stimulus plan.
Murphy, a businessman and political newcomer, secured Obama's endorsement last week when he was named the man who can "turn the economy around and create jobs."
He has also been praised by Vice President Joe Biden for supporting the White House economic agenda.
Obama on Monday signed an email message sent to supporters in and around the district.
"With Scott in Congress, we'll work together to bring about solutions to our economic challenges and create new jobs in upstate New York and across the country," Obama wrote.
"Scott understands the potential we have to rebuild our economy and create a new foundation for prosperity. That's the kind of partner I need in Washington. Please look up your polling place and vote tomorrow."
The Democratic National Committee has also released an advertisement featuring Obama's image that trumpets his support for Murphy's candidacy.
Tedisco, a veteran New York state politician, opposes the Obama administration's economic strategy and has tried to turn Murphy's backing for the stimulus package into a liability.
"It is seen as a very early and tentative barometer of Barack Obama's popularity ... Either as some kind of endorsement of Obama's policies or the beginning of opposition," Himelfarb told AFP.
The vacant seat was previously held by a Democrat, Kirsten Gillibrand, who now occupies the Senate seat left vacant by Hillary Clinton when she became secretary of state.
But the rugged district of forests and mountains was historically Republican territory and new party chairman Michael Steele has made winning back the seat a priority.
A win there, Republican strategists said, would demonstrate wider dissatisfaction with Obama's efforts and spur the party to success in nationwide Congressional elections next year.
Former New York City mayor Rudolph Giuliani said a Tedisco victory would "send a message that the whole (Democratic House Speaker Nancy) Pelosi program has gone too far and that we need to put some kind of responsible brake on it."
"Law and Order" television series actor and former Republican presidential candidate Fred Thompson said the election would amount to a "repudiation" of Obama.
Tedisco seemed on course a month ago when he was 12 points ahead in polls.
But Murphy has roared back and according to a poll by Siena College, he leads by 47 to 43 percent, just outside the 3.2 percent margin of error.
The biggest factor could be turnout, which is typically very low in special by-elections, something favoring the generally older Republican electorate.
According to Himelfarb, that means the pressure is on Tedisco to win.
"If Republicans can't win in this district it bodes poorly for stopping Obama's political agenda," he said.
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