The problem with minimum wages is that they have the exact opposite effect that they are purported to. They actually hurt the working poor, and especially the already-unemployed.
Think about it. If the best job you can get is for $8/hr, what does that really mean? It means that the labor you are able to provide your employer is only worth $8/hr to them. If your labor were actually worth more, then you'd be able to find someone willing to pay you what it's actually worth, and you would already be making for than $8/hr.
A government minimum-wage mandate doesn't change the value of your labor. It increases what the employer is legally required to pay you, but all that means is that now there is a significant gap between what you cost your employer and what you are really worth to your employer. That's a very bad position to be in, as a low-skilled employee.
In the case of fast food, cashiers will simply be replaced by robots. In the case of manufacturing, the plants will move. Service positions that can't be automated - like landscapers or the guys who work at the quicky oil change places - will be eliminated because demand for those services will fall as the price increases in order to pay the higher wages.
It's already happened in Seattle. Just this past year, the number of food service jobs has dropped as many restaurants that have been around for decades had to close, because they simply couldn't afford to pay the higher wages. What does that mean? More unemployed people, more people on welfare, fewer people paying taxes. More vacant buildings, and a higher cost for people who want to go out for dinner.
In the case of EMS, it's hard to say what will happen. The services are going to get squeezed hard because their payroll expenses will go way up while the amount they bill doesn't change at all. My guess is you'll see smaller services leave, and there will be fewer jobs for EMT's and paramedics. A few larger services will remain but working for them will be awful, as they are forced to do more with fewer people and older equipment.