If min wage stays this low your tax money will continue to fund these low wage workers. Put the onus on the employer to pay fairly, let them raise prices, competition will take care of that as will smart consumerism. People can choose to shop elsewhere, more shoppers however, is a clear plus.
"pay fairly" ... my concern is that we are letting the benefits(that were supposed to be short term help) totally dictate what "fair" is, not what the actual job market demands and will bear out.
As to the rest...if baseline prices of things needed to live outpace the wage, which they will - market competition will not fix it. Assuming there will be more shoppers means you assume jobs will be created by a higher wage, which the CBO says will likely not happen.