That is a trite and misleading argument. 89% of minimum wage workers don't live in poor households. To say that they are being subsidized because they are poor is simply dishonest. See my link above.
In the United States, a family of four with a total household income of $23,851/yr. is "not poor". An individual with an income of $11,761/yr. is "not poor".
If you believe an individual can survive on $11,761, or that a family of four can survive on $23,851, in a major city, I would identify that as a flaw in your positions.
the word "households" being key. i just noticed that the text you linked clearly states that in those households there need to be 2-3 workers (or one doing 2-3 jobs) for them to rise above the poverty line. if one would try to put a price on the lost free time, family interaction,.. these people could in fact be in a very tough situation, even though their bank account might not reflect it.
If you believe an individual can survive on $11,761, or that a family of four can survive on $23,851, in a major city, I would identify that as a flaw in your positions.