The NYT had an article on efforts to raise the minimum wage in New York state. At one point the piece gives the views of Russell Sykes, a senior fellow at the Empire Center for New York State Policy, who is identified as an opponent of a higher minimum wage. According to the article, Sykes argued that:
"raising the minimum wage would not be helpful to most poor families. The earned-income tax credit was more beneficial to them, he said, and an increase in the minimum wage could make some families ineligible for the credit."
If a higher minimum wage makes a low-income family ineligible for the earned income tax credit (EITC) it is due to the fact that it has raised their income above the level where they qualify for the EITC. It seems a bit strange to argue that low-income family is hurt by raising their income. The highest EITC rate is 45 percent, meaning that a worker at below the peak (in 2010, $12,549 for a single parent with three children) would get an additional 45 cents for each additional dollar of earnings. If a higher minimum wage raises a worker's income from a point below this level, it is actually increasing the amount of money they get through the EITC, possibly by as much as 45 percent of the increase in the minimum wage.
The EITC then plateaus, meaning that additional earnings neither add to or subtract from the size of the tax credit. For income above $16,450 the EITC is phased out at the rate of 21 cents on the dollar. This means that in a worst case scenario, a worker may lose 21 cents from the EITC for every dollar in additional pay they get as a result of a minimum wage hike.
[This is corrected from an earlier version. Thanks to Robert Salzberg for calling attention to my error.]