Having no state withholding on one paycheck is not a serious problem. It might mean you would get a smaller state refund or owe a small amount of state tax. But you do want to make sure that either they start withholding New Jersey tax or you start making quarterly estimated tax payments to New Jersey. Estimated tax for income that you earn in June, July, and August is due September 15.
Missing state withholding for one paycheck is not likely to affect your federal tax at all.
