No.
For New York, the governor issued an executive order allowing counties to issue their 2018 assessments early, on December 29. Therefore, county and town taxes may be pre-paid on December 29 ONLY (or the 30th and 31st if the county office is open or they have a payment web site.) School taxes in New York are assessed on July 1 of the year. If you have an unpaid balance from July 1, 2017 you can of course pay it by 12/31/17. Some cities bill their school tax in 4 installments, you can pre-pay the January and March installment since the assessment was already issued. But, since the school taxes for 2018 will not be assessed until July, they can't be pre-paid. (And, not all counties are assessing their county tax on 12/29/17. Check your specific county.)
I don't know what they did in New Jersey. However, no state law or state executive action can override Federal law. The IRS interpretation of federal law -- which will stand until someone sues them over an audit -- is that the tax must be assessed in 2017 and paid in 2017. You can't pre-pay a random amount to the taxing authority if they haven't issued an assessment.
