Sometimes it is possible to enforce a loan modification when you have been offered a trial period, made payments and then the mortgage company reneges. The most important thing is that if the mortgage company refuses payments from you, you need to put those payments aside -- do NOT spend the money on anything else. Get together all of the letters and paperwork back and forth from the mortgage company, your payment receipts and the denial letter and contact a lawyer -- preferably within thirty days of when you received the denial.
Foreclosure in New Jersey takes around 270 days. New Jersey is a "judicial" foreclosure state, meaning that foreclosures go through the courts. That means that you can defend yourself against the foreclosure by answering the complaint in writing explaining your defense. If you don't answer the complaint, ultimately judgment will enter against you and the house will be sold at sheriff's sale.
Negotiating with the mortgage company or participating in court sponsored mediation does NOT stop the mortgage company from moving forward with the foreclosure. You should not assume that just because you are trying to work something out that the mortgage company has stopped the foreclosure process.
First things first, I would seek legal counsel, as foreclosure is a very serious matter, and banks are not the easiest entities to deal with. You should especially retain an attorney to deal with the bank's stubbornness as it pertains to the loan mod trial payments.
This being said, however, the notice of intent to foreclose is a required letter that must be sent before suit is filed. It does not mean that WF has filed suit, or if it will even bother. If your house is underwater (i.e., you owe more than it's worth), the bank has an interest in dragging the process out as long as possible, because it won't get the money it's owed at sheriff's sale.
One program that I use with my clients is the New Jersey Homekeeper Program. Simply put, you have the ability to get up to a $48K grant from the government to go towards your arrears, provided you stay in the house for 10 years. We use this money as leverage towards obtaining a permanent loan mod for our clients.