There’s absolutely no way a family with a $52,000 income would pay 30% in taxes. They’d pay $2000, tops (4%), in federal and state taxes combined.
This whole calculation assumes that the illegal guy works full time at $15/hour under the table (very few of them do) and somehow manages to get full benefits.
In reality, Jose Illegal will get $6/hour under the table working full time (if he does not want to work for that kind of money – there are lots out there who do). His alternative is to try to find work as a day-laborer, he’ll be paid $10/hour, but he’s not guaranteed to find any work at all.
With regard to benefits, his children will get free lunches at school, and Jose himself might be able to get food stamps. He most definitely does not qualify for state-sponsored medical insurance (though his citizen children, if any, might qualify). As of one year ago, Medi-Cal does not provide dental coverage at all, even to bona fide citizens.