Our taxable income this year was 34k. That's actually an excellent income for us, it tends to average 25-30k.
HOWEVER, about 10k of that was from investment income that is taxed because we pulled it out instead of reinvesting it. We have a lot of money in investments. What this means is that while we do live very VERY modestly and try (and succeed) to stay within our "income", we have little financial pressure. We can afford to buy our own health insurance. If we needed to, we could pull more stuff and pay off our mortgage within 48 hours (partially because we bought a modest home at a modest price and didn't get some crazy ass mortgage). If an emergency happened, we could deal with it. It would still be stressful, and we prefer not to touch the investments (they are, after all, going to put 3 kids through college/trade school/business startup and fund our old age), and there is a waiting period, but just knowing that that is THERE makes a HUGE difference. Even though we spend far less than most people we know with half or less of our net worth.
So I know that it is possible to do SAHMing (as long as you don't have a huge amount of consumer debt--we had none going into marriage) on a mid 20s to 30s income, I've been doing it for about 10 years now.
However, don't underestimate stress, if it's really tight. In many respects I think knowing that I have $$ makes it easier for me to not spend money, and certainly makes me think about it less, though I think that is a bit counterintuitive.