TRENTON, N.J. — A new poll shows Gov. Chris Christie running for vice president wouldn’t help the Republican presidential ticket carry New Jersey in November.

Wednesday’s Quinnipiac University survey finds President Barack Obama with a 10-point lead over Republican hopeful Mitt Romney in a one-on-one matchup among Garden State registered voters.

Adding Christie as Romney’s running mate shaves off just 2 points for the GOP.

Fifty-two percent of the registered voters compared to 36 percent say Christie wouldn’t be happy as vice president.

The poll also finds incumbent Democrat Bob Menendez continues to hold a 10-point lead over largely unknown Republican state Sen. Joe Kyrillos in the U.S. Senate race.

The telephone survey of 1,582 registered voters was taken May 9-14. The error margin is plus or minus 2.5 percentage points.