James, take this from me - businesses can pay more.
My small business (myself, my partner, and 6 part time employees) makes me just about nothing and I can easily afford more than $7.25/hour on the very little I make. It's not hard to pay them $9.25, which is more than the minimum in Illinois. I pay my employees that because a) they deserve it, b) the better they do their job, the more I can sell, which makes me more money, and if they are getting paid at least somewhat fairly, they have told me that that helps them be motivated to do better, and c) they have bills to pay and deserve to go out to eat every once in awhile or take a nice vacation without the words "Motel 6" coming up. Even paying them $9.25/hour, that still equates to less than $20,000 per year full time, and I don't pay any of them full time because we don't work 40 hours a week.
To make clear what $20,000 a year does, my older sister eats seaweed and rice for her meals, doesn't go out to eat or drink at a bar with her friends, lives in a small apartment in a college town where rent is about as cheap as it gets, and drives a car with 45 MPG and her yearly expenses are, according to my dad (who helps her pay them), about $18,500. That's before taxes, going out to a nice dinner, or buying anything new at all. She is literally the most minimalist person I know that actually lives within civilization and, without kids, she spends that much on herself.
How do you save money making $7.25 an hour? How do you live a decent life making $7.25 an hour? How do you pay for a kid at $7.25 an hour? How do you go on vacation? Okay, maybe you don't do any of these things. Even so, how do you replace your car battery if it dies? How do you pay for the doctor when you break your arm? How do you pay to fix your heater before the winter?
The real question, though, is how do you position yourself to advance in the world and break the cycle of poverty and hopelessness? At $7.25/hour, you don't save money, you don't invest money, you don't put money in a 401K, you don't start a college fund for your kid, and if you didn't graduate and are stuck, you don't have enough money to pay for college yourself so that you can get out. It's a giant trap.
If inflation is 2% (I have no idea what it actually is) and the last increase was in 2009, then $7.25 is worth 14% less than it was then. Next year, it will be 16%. By 2020, it will be above 20%. We have a minimum wage for better or for worse, we have inflation for better or for worse. If the goal of minimum wage is to provide a baseline that someone - ONE PERSON, without a family or kids or whatever - can *live* on, then it needs to rise accordingly with inflation.