All of this is entirely false. It ignores the reality that if businesses could simply lay people off or cut hours and achieve the same output then they already would have whether you raise the minimum wage or not. You need a certain amount of man power to run a business. You can't just arbitrarily change that because you feel like it.
While I cannot operate a store with fewer than one employee per every opening hours, I still can cut on opening hours. Likewise, if I planned on opening new shops, the fact that the labor cost of a peculiar way to organize the production of my service would rise might tip the scale against the case for opening that shop. This isn't just a theoretical curiosity: people really do open businesses to turn a buck and anyone trained in management knows how to compute the net present value of hypothetical flows of income and expenditures. The crude fact of the matter is that a rising price tag for labor that is not matched by an increased production capacity makes using this labor less profitable. That has to be factored in some way by people who obviously are looking for opportunities to earn money.
That some people will simply eat up their profit margins to cope with the increased labor cost seems reasonable. Some reasons might include the one you mention (a floor for maintained activity), or even adjustment costs that make changing how a business operates too costly to incur. However, it is not clear that this ought to be the case in every case, let alone in a majority of cases. Even combining your claim with the adjustment cost mechanism I pointed out above, there remains the question of how strong it can be thought to be. That is an empirical question and Card's 1990 paper certainly allow for that possibility. While it seems a little far fetched to me to just assume away potential bad consequences that seem so obviously tied to a policy, we do not have to do any such thing. Just use the cities that already enforced a very substantial hike as a treatment group and use a difference-in-differences estimator to capture the effect on hours worked, job creation, job destruction, etc.
The profit margin for many corporations easily allows for them to give the raise in salary without increasing prices.
That sounds like a presumption to me, but let's assume in good faith you're not just throwing this around. Where did you get that information? Even crude approximations of how businesses operate require knowing quite a bit of detail from their financial statements. My statements above are all conditional, or at least are intended to be taken as conditional. I have no precise idea what every single business, or even what a substantial fraction of them, can or cannot do.
The bottom line is this. We have increased the Federal Minimum wage more than twenty different times since the 1920's and yet here we are with one of the strongest economies on earth and pretty close to full employment. If raising these wages was bad for the economy then why does it keep getting better even after all those increases over the decades.
I don't think anybody says it will bring the whole country to a halt. To the extent anyone does, let me express my doubts. However, given these events, we can statistically look into the issue and answer the aforementioned issue of having to compare many mechanisms that operate at once, often in different directions. Most of what I know in economic theory would suggest it will have a depressing effect and that includes Morgenstein-Pissarides types of model that involve search and matching (i.e., here, transactions are costly and wages are negotiated depending on negotiation powers between firms and employees). It is not surprising: you're making the price tag heftier, but you don't change production capacity. There are exceptions, however. If you make sufficiently constrained choices, the type of dynamic you have in mind might just make sense. If I have to make a binary choice between not having a business and having a slightly less lucrative business, I might just eat my profit margin and shut up. You can make this story more complicated, but anything resembling this is going to say the minimum wage will just shift resources from business owners to employees.
