The district's new boundaries have yet to be determined, as New York is engaged in a messy redistricting process mired in legal complaints. But Democrats also polled outside the district but within the county, suggesting even if the boundaries change, Bishop will start off better-known and liked among voters in other parts of the county.

Bishop had just under $1 million on hand for his reelection at the end of September, while Altschuler had about $400,000 — but also $500,000 in debt, which his campaign says represents funds Altschuler lent his campaign during the last cycle.

George Demos, a former Securities and Exchange Commission prosecutor who ran against Altschuler in the 2010 primary, is competing again in the GOP primary, and had about $75,000 on hand.

"Randy Altschuler couldn't win in a year Republicans couldn't lose. He's simply unelectable," said Kevin Tschirhart, Demos's campaign manager.

The poll of 501 likely voters in Suffolk County was conducted using live telephone interviews between Oct. 16-18 and had a margin of error of plus or minus 4.4 percentage points.

- This post was updated at 1:53 p.m and 3:54 p.m.