Raising it only kicks the problem further down the road. The minimum wage needs to be tied to the local average cost of living and dynamically adjust on a year to year basis accordingly to accomplish the original goal of allowing a full-time worker to support themselves on it. Without dynamic yearly adjustments, inflation and political apathy will simply put us back in the same place 10 years down the road.
This is the fight we should be fighting, not for a number, but for a law that makes it illegal to hire someone at a wage below the cost of living.
Under federal law, you can work 2 full time jobs, 80 hours a week, and still not make $120/day ($120 = 8 hrs x $15/hr). $15/hr isn't insane, it's not even bare minimum anymore.