On June 20, the New Jersey Supreme Court declined to hear the case that challenges the October 16 date for the special U.S. Senate election. See this story. This makes it certain that the election will be held in October. There is a bill pending in the legislature to move the November 5 election for state office to October 16, however, so it is still conceivable that New Jersey will just have one important general election date this year instead of two.
A general election is when all offices are up in general. An election with a single office is a special election.
Senator Lautenberg died the day before the primary. New Jersey will have managed to have a filing period, a senate primary, and a senate election, including time to send ballots overseas, and be finished a month before the general election. In fact, New Jersey even has time to consider moving the general election earlier.
The primary is simply too early.