A lot of people will discover that they have a lower net income, after their minimum wage is increased. This phenomenon is known as the "welfare trap" (think of the trap under a sink, and you'll get the idea.
Taxes are not the only claw-back for low-income wage earners. A host of social-welfare programs have claw backs too (e.g. you pay more for Obamacare, if your gross income increases). The "effective marginal tax rate"* for low income workers, varies from over 50%, to over 150%. That's right -- take home pay can decrease as wages increase.
* If the government takes something back, that's "effectively" the same as a tax.
There's quite a bit about the "welfare trap" (aka "poverty trap") on-line. Here's a link to a good article: http://www.heritage.org/research/testimony/2013/06/what-is-minimum-wage-its-history-and-effects-on-the-economy
That article lacks good graphics. Here's a graphic that shows how net income decreases sharply, as lower wages pass a certain threshold:
