N.J. Stat. § 19:3-26
If a vacancy shall happen in the representation of this State in the United States senate, it shall be filled at the general election next succeeding the happening thereof, unless such vacancy shall happen within 70 days next preceding such election, in which case it shall be filled by election at the second succeeding general election, unless the governor of this State shall deem it advisable to call a special election therefor, which he is authorized hereby to do.
The governor of this State may make a temporary appointment of a senator of the United States from this State whenever a vacancy shall occur by reason of any cause other than the expiration of the term; and such appointee shall serve as such senator until a special election or general election shall have been held pursuant to law and the Board of State Canvassers can deliver to his successor a certificate of election.
N.J.S. § 19:3-26