http://www.atdn.org/access/poverty.html
In my area, you can't buy a house for less than $40k (I've looked and kept looking, that includes 2 bedrooms). That's a house payment of $400/month (with property taxes and insurance). So $4,800. To rent an apartment is considerably more - for a family of 4 you are required by law to have a 3 bedroom apartment (unless both kids are the same gender). A 3 bedroom apt is $500/month, plus you need to buy renters' insurance and it doesn't include utilities. But we'll stick with $4,800.
Plus there is SS tax on the income (the poverty levels are pretax dollars) so for the family of 4 that's $1,175.
Then you have health insurance (since most jobs paying poverty level don't pay health insurance or only pay a little). For a family of 4 the cheapest health insurance I could find was $489/month. We'll assume that I just couldn't find the best insurance and cut that to $400/month - another $4,800.
Then you have utilities. The minimum payment for electric is $25 (that's the absolute minimum they will charge). The lowest electric bill I've ever had (840sqft home, no AC) was $40/month - $480. Trash and water is $25/month minimum (and you have no choice but to have garbage service in most cities) - $300. Phone of some sort (you need some sort of phone for emergencies because you can't rely on your neighbors or payphones - assuming you can find a payphone) minimum $25 - $300.
That leaves $7,495 for food, doctor visits, transportation costs, clothes, school supplies, etc. $625/month sounds like enough for that, but that's if all your expenses were kept to the absolute minimum, which never seems to happen as much as you try your hardest.
Most people making poverty wage collect WIC and medicaid insurance for their kids. That's a form of welfare.