http://www.njlawnet.com/njlawreview/eviction.html
NON-PAYMENT OF RENT
If a tenant fails to pay "rent" when due, a landlord may immediately proceed to commence a summary proceeding to regain possession of the premises. A landlord is under no obligation to wait for its rent, accept payments late, or accept rent in installments. However, if on the "return day" (day of court) the tenant appears and is prepared to pay all "rent" which is due, the landlord must accept the tender and dismiss the case. N.J.S.A. 2A:18-55 provides:
N.J.S.A. 2A:18-55. Discontinuance upon payment into court of rent in arrears; receipt
If, in actions instituted under paragraph "b" of section 2A:18-53 of this title, the tenant or person in possession of the demised premises shall at any time on or before entry of final judgment, pay to the clerk of the court the rent claimed to be in default, together with the accrued costs of the proceedings, all proceedings shall be stopped. The receipt of the clerk shall be evidence of such payment. The clerk shall forthwith pay all moneys so received to the landlord, his agent or assigns.
(Case Law has held this statute is applicable to proceedings under the Anti-Eviction Act as well. (N.J.S.A. 2A:18-61.1.))
I have put "rent" in quotes in the preceding text because it is technically a legal term that should be defined. In a broad sense, it is the compensation or fee paid, usually periodically, for the use of any property, land, equipment or building. However, if a tenant agrees that certain charges constitute "additional" rent (i.e. utilities, damages, late fees) a court will likely enforce the agreement if it does not conflict with any statute, rule, regulation or ordinance such as rent control or U.S. Dept. of Housing & Urban Development regulations ("H.U.D.").
Like almost any rule, there is an exception to the "no notice rule" for non-payment of rent cases. When filing a non-payment of rent case against tenants receiving (1) social security old age pensions, (2) railroad retirement pensions and (3) other government pensions, these tenants are afforded a 5 day grace period to pay their rent, presumably because their checks are sent to them on or about the first day of each month. (copy of the statute appears supra.) Likewise, tenants who participate in a H.U.D. subsidy program are entitled to the additional protection of federal laws that require a written notice be served upon the tenant prior to the filing of any action for eviction.