Yes, it is possible to get a ticket in New Jersey for a cracked windshield.
New Jersey Motor Vehicle Commission (MVC) says as a driver you are responsible to have a clean windshield, one clear of chips or cracks. If your vehicle does have a crack in its windshield, it depends upon where the crack is located on the windshield and the discretion of the New Jersey police officer if you will be ticketed or not.
The New Jersey Statutes discusses windshield and safety glass in Title 39 subsection 3-75. Here it says in part that your windshield should have "no undue or unsafe distortion of visibility or be equipped with unduly fractured, discolored or deteriorated safety glazing material" when you are driving your vehicle.
As you can see, New Jersey law 39:3-75 leaves it open then for a law enforcement officer to use their own discretion and judgment to determine if a crack in a windshield is unsafe and warrants a ticket or not. If you are cited for your cracked windshield the fine amount under this portion of law is right around $55 and does not come with points assigned to it.
Equipment tickets like this typically will not cause your car insurance rates to rise, but it would be up to the rating system of your auto insurance company. If you are ticketed and your rates do go up, it may be time to shop compare insurance companies and find lower rates.
If you have comprehensive coverage, then a cracked windshield would be covered. You would need to pay your deductible and then the remaining cost of the windshield repair or replacement should be covered by your comprehensive coverage.