Thomas Kean Jr., the Republican, and U.S. Sen. Robert Menendez, the Democrat, are in a statistical dead heat, with 40 percent of those surveyed saying they would vote for Kean and 40 percent preferring Menendez.
Many of those who support Kean said they liked him because of his father, a popular two-term governor who is currently in the limelight as head of the panel investigating the Sept. 11, 2001, terrorist attacks.
"The fact that I like his father has a lot to do with it," said Robert Sapanara of Ramsey, N.J. "I think there's got to be some counseling given to him by his father and hopefully some of those genes rubbed off on him."
If his father helps Kean, President George W. Bush hurts him, the poll found. Menendez backers said they want a Democratic majority in the Senate.
New Jersey is one of a handful of battleground states in the struggle between Republicans and Democrats for control of the Senate.