Candidates for New York's 26th Congressional District, Republican Jane Corwin, left, and Democrat Kathy Hochul. (AP Photo/Derek Gee - Buffalo News)

According to House Democratic leaders, the answer is yes – but only if the Democratic candidate wins.

Polls have shown the Democratic nominee in the three-way race, Erie County Clerk Kathy Hochul, competitive against Assemblywoman Jane Corwin (R). For weeks, Democrats have been arguing that the race is a referendum on the House Republican budget. Republicans have pointed to polls indicating that independent candidate Jack Davis may serve as a spoiler.

“Clearly, in New York, the issue -- as (Democratic Congressional Campaign Committee Chairman) Steve Israel likes to say, there’s three critical points about that race: Medicare, Medicare and Medicare,” House Democratic Caucus Chairman John Larson (Conn.) said at a news conference Tuesday morning after a House Democratic closed conference meeting.

House Democratic Caucus Vice-Chairman Xavier Becerra (Calif.) added that the race is “probably the best indicator of what the American people think about the Republican agenda so far this year.”

“We would not be where we are today in New York watching an election where, for perhaps the first time this year, the American public will send a message to the House Republican leadership about having the wrong priorities,” Becerra said of the race for the Republican-leaning seat, which was last won by former Rep. Chris Lee (R) in November with more than 70 percent of the vote.

Of course, history shows that it can be dangerous to read too much into any special election. Nearly one year ago today, for instance, Republicans won a special election for a House seat in Hawaii, with two Democratic candidates taking second and third in the three-way race. President Obama had won the district in 2008 with, yes, 70 percent of the vote. (Democrats later regained control of the seat in the 2010 midterms.)

What happens, then, if Republicans end up winning the seat when polls close at 9 p.m. tonight – would the race stand as an affirmation of the House Republican budget plan drafted by Rep. Paul Ryan (R-Wis.)?

Not necessarily, Becerra said, pointing to several moderate Republican senators who have recently come out against the Ryan budget plan.

“Well, probably the best answer to that question is what Sen. Scott Brown said, what Sen. Murkowski recently said, Sen. Snowe recently said. They have all come out to say that the Ryan plan, the Ryan budget, the Republican budget that goes after Medicare, is not what they would support,” Becerra said.

“Kathy Hochul is going to win this because she’s just a great candidate,” he added. “It so happens that Republicans have given the Democrats a great issue to really highlight to the American public the differences between Democrats and Republicans. We’d like to improve Medicare; they’d like to put an end to it.”

House Majority Leader Eric Cantor (R-Va.) told reporters Monday that he believed the race was anything but a referendum on Medicare.

”(Corwin) is facing a three-way race that has tended to make the race a lot closer than anyone had thought,” Cantor said. “But, no, I do not think it can be seen as a signal as to the role of the budget reforms that we have proposed, including Medicare.”