I was skeptical when you suggested that it was that small, but the most recent Pew study says that only 2% of workers earn the federal minimum wage in the U.S. [1] But they go on to point out that 30% of American workers earn "near-minimum wage" i.e. ≤ $10.10/h. If minimum wage were increased to $9/h, that would probably affect the earnings of nearly all of those people.
[1]: http://www.pewresearch.org/fact-tank/2014/09/08/who-makes-mi...
It's not enough to get the people at the 5th percentile to where the people at the 25th percentile are. We need to get the people at the 25th percentile to where the people at the 50th percentile are now, and the people at the 50th percentile to where the people at the 75th percentile are now etc.
Trying to lift up only the bottom is what hollows out the middle. We need to lift up the middle too.
I believe every additional $1 of income for the lowest income leveled created economic growth of $1.40 or something and as you got to higher income brackets it hit parity with $1, then finally was significantly less than a dollar.
The minimum wage is an old rally flag, but it affects the bottom 1% when the problem is the top 1%. It's not the difference between the 1st percentile and the 25th, it's the difference between the 25th (or even the 90th) and the 99.9th.
The policies to fix that aren't the "help the poorest" ones, they're the ones that help small businesses and help consumers. Trust busting, lower housing costs (especially middle class housing), reducing regulatory compliance (paperwork) costs on small business, government spending on infrastructure, municipal fiber, patent-free basic research funding, etc.
Minimum wage is a distraction from the things that would actually help.