You are exactly right.
Most of these illegals come here and leave their family back in Mexico where the cost of raising and providing for a family is much cheaper.
A bunch of them will pool their money and live in a trailer or an apartment and split the cost. That's why they can work so much cheaper.
They also don't have to pay income tax, social security tax, or state income tax, or property taxes, or house insurance, or auto-insurance, or buy car tags, medical insurance, etc: that the American citizen has taken out of his check, or has to pay trying to provide for his family that's living here.
Six or seven American dollars will by a lot more necessities in Mexico than they will in Dallas, LA or New York.
Until they learn about the overly generous government housing subsidies, free breakfasts and lunch at the free schools, free health care, free baby sitting services at Head Start, food stamps, WIC and all the rest. Then they realize that by bringing the family here, the low wages with no health insurance benefits will go much further here than supporting the familiy in Mexico. Then they want amnesty and legal status to make it easy to get all that and bring in their extended families.