Wouldn't a conservative believe that employers should be paying their employees enough so that they can feed their families so that taxpayers don't have to step in and make up the difference?
No, a conservative would believe that the, and I'm going to use a term here that will send shivers down your spine, "FREE MARKET" should determine what an employer will pay their employees. Minimum wages do nothing except spur on price hikes for those employers most affected by their implementation.
For example, I am not so worried about a big national chain that has to pay minimum wages, they can make up a lot in quantity, what I am worried about is the mom and pop hamburger stand on the corner that is forced to pay a high school student minimum wage. At $7.00 an hour, at 20 hours a week, Susie Cheerleader is earning $140.00 a week. Now tell me that somehow you have helped the "working poor" when you force a mom and pop hamburger stand to meet that minimum wage. You haven't, and you know you haven't. You haven't saved anyone. What you have done is interject the Federal government into the mix which only drives up the price of that hamburger and will, in the end, make mom and pop think twice about hiring Susie Cheerleader.
Jobs that are traditionally low-end should be used as a spring board for gaining experience and education where you can get to those jobs that do pay more. Take a young man that comes out of high school and doesn't want to go to college. He takes a laborers job at a construction site. Yep, the pay is going to really suck. If this is the limit of his aspirations then he is really stuck working for what that construction company will pay him. As he learns he may become a carpenter, a framer, or work with concrete or something. Experience and ability will guide his wages. BUT, while he is working construction, if he goes to trade school and learns to say weld, when he completes that school he has a job waiting that starts at $60,000 a year.
Where the problem occurs is when you have those that have NO EDUCATION and NO DESIRE to actively pursue something better. Because you think you have a big heart, you want everyone to be paid a living wage for picking up trash. If they do, you take away one of the biggest motivators to make yourself better. That is the problem with trying to "help". In the end you don't help them, you just enable them to stay at a low-end job.