During the 1990-1991 wage increases - of those who earned between the old and the new minimum $3.35 and $4.25 only 22% lived in poor families. All told including no or small employment effects [reduced employment due to higher wages] only 19% of earnings increases went to poor families, mostly going to workers in non-poor families. Seems like a blunt instrument to fight poverty (ref)Now, you might think it's OK that it's such a blunt instrument. The legislation does put some money in the pockets of the poor. The wasted money goes to the non-poor (probably teenage children or other dependents in non-poor families). The cost of the program is hard to say but it is highly likely to involve both loss of some jobs (both for the poor and for non-poor working near the minimum wage), and in higher product prices (which may affect poor or non-poor). However it becomes harder to justify the costs of the program since so many of the possible benefits of the program are wasted.
Another rationalization would be to say that the raise in wages to the non-poor working near minimum wage is still a real benefit. Still, it's worth considering whether that benefit is worth the cost. Personally, I prefer programs that help the poor but also have very low waste and market distortions. A tax credit only for the poor would probably fit that description.