No, I wouldn't support lowering minimum wage.
I support kids in high school or retired people to make minimum wage and even college students making minimum wage.
But if you are 35 years old, have 3 kids and a spouse while making minimum wage for the past 10 to 15 years, that's on you and no one else.
Minimum wage is entry level work, it isn't supposed to support a single person who lives on their own or a couple and it's definitely not going to support a family.
Find a job, start on the bottom level and work your way up...the way it's supposed to be done. Stop taking basket weaving in college, if you can't hack it, go to a trade school, get a simple business degree to get your foot in the door with a good company, stop trying to get everyone else to pay for your ignorance.
I filled out an application a long time ago to work for Proctor and Gamble in Cincinnati. I got an interview and was almost hired until the interviewer noticed I had no college education. He told me, "You need at least two years of college to work here, I'm sorry but we can't hire you." I asked him why I needed two years of college to drive a forklift and he said because when you move up, you will be required to use that education.
I never got my two years of college education but I wish I did. P&G stock has split multiple times since then and they have stock options, lol.