I do not think that is necessarily wrong.  They are two very different things.  I was a New Hampshire State Representative and had to vote on bills concerning minimum wage.  A minimum wage is just that, the lowest wage that you can pay anyone, including a teenager at their first job.  I preferred to let the marketplace set wages, so I was in favor of a lower minimum wage.  If the minimum wage is high enough to meet the needs of a single mother and her children with no other income source, it would be too expensive to hire that teen.  Additionally even if one believed that a minimum wage job should be enough to survive on, that would need to be based on a two person family income.

In my area, to live the leanest, (no car, cell phone or entertainment ect.) a family would need at least $500 a week.  If you based the minimum wage on that you would have a minimum wage of $12.50.  I do not think most states are that high, if any.

Raising minimum wage up to livable wage has another problem.  Many workers contracts call for their wages to be a certain percent over the states minimum wage law.  As minimum wage laws rise so does a significant portion of the population.  This not only makes it harder for business and government to survive, it also fuels inflation, by higher prices for goods and higher taxes to cover the cost of higher wages.

Because of these reasons, minimum wage should not be a factor in setting a state's welfare rates.  It is up to each state to set a policy as to what it costs to live in a given area and how much it wants to help families in need.  (In my opinion welfare families should not do better than working families.)  If we want to lower welfare costs, we should teach abstinence and enact measures to encourage traditional families and keep them together.  This will lower the number of families that need welfare.