Conservative opposition to the minimum wage is based on the general conservative position that tampering with the open market is never a good idea. Labor is something that is bought by the employer and "sold" by the worker in the same way as any other item. Its "price" depends on how much it is in demand (more demand, a higher price) and how much of it is available (more availability, a lower price). Wages for unskilled or slightly-skilled work are low because there are plenty of people available who will do that work for that low price and there are enough employers willing to hire them for that rate. If the government requires that that price be higher -- the minimum wage -- employers will be less willing to buy, in the same way that if the price of milk goes up, fewer consumers will purchase it. Employers can buy less labor in two ways: they can hire fewer workers or they can keep the same number of workers but reduce their hours. In either case, the workers are worse off than they were before. Those who are viewed as the least educated or the least dependable employees will be the hardest hit, including African-American males, former inmates, and other groups.  Therefore, any minimum wage or minimum age increase, though well intentioned, has unhappy consequences. 

Quick arguments that minimum wage increases inevitably hurt employment usually overlook two key points. One is that the amount of the increase makes a difference; obviously, a small increase will have much less potential impact on employers than a large one, since employers can make cost adjustments before cutting back workers if the increase is small. The related factor is that any potential impact would depend on how high the existing minimum wage is in relation to the national average hourly wage (currently about $21). If the minimum wage were 50% of the average hourly wage, which would be $10 or $11, there would be a stronger case that this minimum wage -- and any increase -- is too expensive for employers than if the minimum is around only 30 to 35% of the average wage, as it is today. Usually both factors -- the amount of the increase and the level of the wage in relation to the average -- remain on the low side, since modest increases are more likely to become law than large ones.