Apparently, they don't need help. You are making up a scenario to fit your preconceptions. The 15 will be gradually installed. Working costs money. You need childcare, transportation, food, and work clothes. You seem to not give any thought to the worker.
That is not a made up scenario but the older man and wife (both with medical problems) who ran the small cafe at the college where I worked for 40 years. They could not handle the breakfast-lunch crowd alone and needed a student worker who was partially subsidized. They took their food truck to events on week-ends to make a living.
To tell that couple they could not have a business because they could not afford $15.00 an hour (more than they made together) is not caring about the worker. FDR had no clue what the small worker goes through.
The best advice to give to (potential) workers is to get training, education, or experience to qualify for a living wage. Not only do they make more money but they get better benefits and probably have more job satisfaction. That is caring about the worker---not just giving him more money by possibly hurting small business owners.