How does ANYONE come up with a down payment for a home (on their own?)

I'm feeling a little bit "woe is me" at the moment as I see my friends all buying homes, while I see no way in the world that we will ever be able to come up with any kind of down payment.

I have a good job (I'm a CPA) and my husband works as well. We had some savings, but it was all eaten up by my preemie son's birth and other medical bills (which are still a constant drag on our finances). We have stopped going on trips, eating out - we don't buy expensive coffee in the mornings. We don't have investments we can cash in, or big credit card debt dragging us down, or family that can spot us the cash. All of the "how to save money" tricks? We do them. Yet we're still living paycheck to paycheck.

How did you come up with your down payment?

EDITED TO ADD: Where would I go to speak to someone who can help me understand how much I'd actually NEED for a down payment? A bank? an outside lender? a financial planner?