The ideal number is zero. The safety net should be tied to the earned income tax credit, subsidized health insurance and housing, school and food stamps/vouchers - exclusively.
But what would stop a private business from offering employees $1 a day, noting that by working full time they will get all the paid benefits on your list? Wouldn't that just amount to the employer shifting their labor costs to the government and thus to the taxpayers?
Good point, which I have thought about. My fix, is that FICA etc would be based on a minimum wage concept, so the employer pays a certain amount for that, even if the wage rate is otherwise too low per the formula. In the end, competition for labor will mitigate your concern, except to the extent employers then pay cash under the table. So the incentives have to be there not to encourage tax fraud. That is one way to do it. And the phase out of the benefits should start early, so the employee always gets a bit more net from a higher wage. In the end, if 99% of the workers, really do produce a value added in a given zone of at least say 5 bucks an hour, then sure, set the minimum wage at that. Then there is no real legitimate market for lower wages, other than for purposes of gaming the system. The perfect can be the enemy of the good.