This poll, however, might be added reason for the senator to decide on his future plans for office. The 88-year-old is considered a top retirement risk for Democrats.

He has not given any indication if he will seek reelection in 2014, however, and Booker's early indication that he would be willing to mount a primary challenge against Lautenberg was met with private frustration from some New Jersey Democrats.

Booker has ruffled the feathers of Democrats in the state in deciding to run for Senate rather than in the gubernatorial race; his decision not to challenge Gov. Chris Christie (R) was seen by some as personal promotion at the expense of party success. The race against Christie is likely to be a much tougher one for a Democrat to win than a Senate seat, long held by a Democrat, that may be open.

The survey, conducted among 700 voters statewide from Jan. 2-6, has a margin of error of plus or minus 3.7 percentage points.