In New Jersey, pregnancy and childbirth is considered a temporary disability covered under the state disability benefits.
According to the New Jersey Temporary Disability Insurance FAQ, you have 30 days from the first day of disability to file a claim:
Is there a time limit for filing a disability claim?
Yes. You have 30 days from the first day of disability to file your claim. If your claim is received more than 30 days from the start of the disability, you must show good cause why the claim was not filed timely. You can attach a statement to the claim form (DS-1) explaining why your claim is late. If good cause is not shown, benefits may be reduced or denied.
For a normal pregnancy, the first day of disability is generally 4 weeks prior to the expected due date.