I'm seeing what is happening, in my own country, as we have just had a rise in the minimum wage. Businesses are not failing because of this, as many pay above the minimum wage already, (as we do in my own business). So the increase is already absorbed. If the only way my business could survive, is by paying the minimum wage to staff, then I have no business being in business.
The problems in your economy, that prevent businesses from being viable if they have to pay a small increase in the minimum wage, are caused by allowing your country to be run by large corporations, for the benefit of those already wealthy, and the shareholders of those corporations.