I think that you need to call the New Jersey State Labor Board to find out if your job could do that. They have to have some sort of jobs that would not require lifting, answering phones, doing paper work, sweeping up or cleaning, something to keep you working.
As for the claim on the insurance...I can't imagine that you could get any sort of disability for being pregnant since it's a choice...not saying you are to blame or anything like that, just that pregnancy is a normal thing and not a disability.
The labor board can tell you what the law says about this.
As a last resort their are state programs that can offer some assistance, I know they won't be near enough though. But at least you wouldn't be going hungry if you got food stamps to help with the grocery bills.
ETA
I agree that perhaps finding another job would be a good thing to consider. I can say that I know of several people who have been pregnant and left for maternity leave when they had the baby. When they called after their 6 weeks off some didn't have a job to go back to because they had to hire someone to take their place and they were doing a good job so they couldn't just fire them too.
One came back, had the infant in a child care setting but when she went to check the schedule for the next week's work she was on the night shift, 11pm-7am. She told them she had to work her regular days due to child care and none took babies during those nighttime hours. They said take it or leave it. They did not have to return her to the same job, shift, or anything. She chose to get pregnant and leave work. She tried to find child care and could not so she had to quit. Since "she" quit she could not draw any benefits due to being out of work.
Another friend got off to have her baby and they told her she could have her job back when she was ready. It was a call center open 24 hours per day. When she came back to check the schedule they too had put her on an evening schedule from 6pm-2am. No child care for her either.
So even if they worked with you the job you'd be coming back to might not be the one you left or even the shift you need or anything.
Finding another job that would be temporary until you deliver might be something that would work for the interim until you can seek full time employment.