Hi,
I'm not a lawyer but I've been in your shoes with a newborn.
I was laid off the day my maternity leave ended. I was floored and quite scared too. I learned it may be illegal for them to lay you off (without due cause) - you can try to get a severance package, you can file a lawsuit for discrimination (or not, I didn't) and you can file for unemployment benefits immediately with your state (the amount varies but it will help you get by). It's not government assistance, it's your right to receive this money if you've lost your job (not if you quit).
Do this immediately, even if you were just unceremoniously called to be told the "news" and no pink slip was given. It's not necessary. The clock starts ticking when you lose your job and it's not retroactive. You can file for unemployment online, from home, you may or may not be called for an interview ( I wasn't) but it's far easier than I thought it would be.
Keep all records. And start looking for a job immediately. If I remember right you need to send out at least 10 resumes a week - you need to be actively searching for a job to get unemployment.
You need to prove that you have been searching, so start your job search on monster.com initially. I found it had the best jobs and I was able to send out the resumes easily and print out the jobs I had applied to and when. if you do it by classified, it's harder but I used to mail these with "proof of mailing" at the post office. Delivery confirmation (with priority mail) was just too expensive at $5 per resume - it adds up.
Being pregnant (or with a newborn like I was), the job search might get tricky, though, depending on how far along you are. I don't think they can ask you if you are but if you are pregnant and there are a lot of candidates, the hard reality is that they may not consider you. Legally they can't do but that's what they do, there's no way to prove it alas. Not all employers do this, some might.
Keep records of any call backs or interviews you've had. Who you spoke to, when. Interviews you've gone to. Send thank you note and hopefully you will get a job offer. If not, unemployment will cover you and keep paying benefits - I think its 12 weeks from the date you lost your job.
In my own job search, I sent out a ton of resumes, got a few vall backs and was able to get two offers in different fields near the end of the 12 week period, but one had very long hours (including weekends) and another was a very low-paying position where having my child in day care (at the same location) would net a grand total of $6,000 a year for working, after deducting the cost of daycare.
When unemployment ran out, I was very worried but was given a chance to extend the unemployment benefits. It meant keeping up with the job search and by this time I realized we would probably be better off being a stay at home mom and reducing our living expenses to a minimum. I decided to stop looking for a job, and yes, this meant no more unemployment benefits.
We were fortunate I was on my husband's health insurance when baby #1 was was born (my employers insurance was lousy and I had switched) but I believe you can apply for an extension of coverage for your own health insurance if you lose your job (Cobra)
http://www.dol.gov/dol/topic/health-plans/cobra.htm
When you lose your job it's surprising how many friends and relatives can come to your aid. Don't be ashamed of telling people, it happens to all of us and it's absolutely understandable. I've been laid off twice so far - once when I was on my own and my company went bankrupt, and I couldn't afford rent anymore - a kind friend let me stay with them and in turn I helped her by taking care of her baby. When my husband was laid off years later, we moved in with his family (sounds like a bad idea but it worked out well) and we stayed with them for a year, long enough to be able to save some money to get a small place of our own.
And somehow, even though it seems as the floor has caved in under you, tomorrow will be another day. I know it seems like a roller coaster but after 20 years of working and several layoffs, somehow we've found out that when one door closes another one opens. Grab opportunities that come your way, this might be God's way of nudging you to guide you to a better path in life, even if you don't quite understand it now. Everything happens for a reason.