“My question is what stops the min wage from causing a trickle-up effect throughout the entire spectrum of incomes?”
Nothing stops it and it will certainly happen as it has happened before. In addition to many, many layoffs which the increase in the min. wage will cause there will be a whole lot of unhappy workers who after working hard to elevate their wages see untrained and unproven new hires earning exactly what they are. These employees will want more in wages and if they don’t get it they will begin looking for another job.
If the employer wants to keep the worker he will either pay him more and if cannot afford that he will simply lay off another worker so he can afford it.
In the end wages are always determined by the market and are a function of supply and demand.