Who Earns Minimum Wage in the United States? Heads of Household?

In his State of the Union Address this week, President Obama said, "And to everyone in this Congress who still refuses to raise the minimum wage, I say this:  If you truly believe you could work full-time and support a family on less than $15,000 a year, try it.  If not, vote to give millions of the hardest-working people in America a raise."  But is the minimum wage really about heads of household?  Who earns minimum wage?
According to the Bureau of Labor Statistics, The following facts are true about 2013 (numbers are in thousands):

Number of hourly wage and salary workers:
75,948
Number at or below minimum wage ("minimum wage workers"; includes those receiving overtime pay, tips, or commissions):
3,300
Number of minimum wage workers age 25 or over:
1,638 (50% of minimum wage workers)
Number of minimum wage full-time workers:
1,173 (36% of minimum wage workers)

No direct data is given for the number of full-time minimum wage workers age 25 or over (most likely to be sole or joint breadwinners).  No data is given regarding tax filing status (to determine how many workers are heads of household).  Insufficient data is given to say with much certainty anything other than the following statements:

The number of full-time minimum wage worker heads of household earning only the minimum wage (no tips or commissions) is likely much less than the number 25 or over and much less than the number of full-time workers.

The number of full-time minimum wage worker heads of household earning only the minimum wage (no tips or commissions) is likely less than portion of those age 25 or over times the portion of those working full-time.

In the absence of data about filing statuses or tips and commissions (all of which would contribute to a lower estimate of those households solely dependent on a single minimum wage job), I can only guess that less than 20% (50% * 36%) of minimum wage workers are heads of household.  That is 0.9% of all hourly wage and salary workers.  I cannot guess how many are sole breadwinners.