I live in the state of Washington and our minimum wage is currently $9.19 per hour, the highest in the nation. Most min wage jobs don't offer benefits until after working there for atleast 6-12 months and even then the coverages are minimal to say the least and only for the employee, not their family. Many of those employers are fast food and lower quality retail jobs with less than decent working conditions with high turnover rates and usually only part-time jobs that don't qualify for any benefit coverages. Here the cost of living is also very high. Most welfare recipients don't have the qualifications for better jobs. Even entry-level jobs(office or trades) require some current experience and/or post high school education.
If you happen to be a young mom with a kid or two or more, it's really difficult to find a place to rent, utilities, food, clothes, childcare, transportation costs, etc with a minimum wage job. Anyone in that situation can usually qualify for some welfare assistance with some of those expenses, but not enough for them to live decently. Even with the childcare costs, the state will cover a majority of the expense but not all of it It's even more difficult to find any childcare for nights or weekends (retail & fast food jobs usually require those shift) and the few that are, are booked with waiting lists and charge a higher rate. Most subsidized housing also has about a 3 to 4 year waiting list. And currently jobs, even minimum wage jobs are getting harder to come by.
Compare all that with full welfare benefits, food stamps, 100% medical coverage for yourself and family, the government makes it very difficult to justify getting a job and getting off welfare when it's more beneficial for the recipient to stay on. Although for most, there is a five year cap on benefits for life and in order to qualify for TANF they must comply with job finding and/or education/training requirements.
I'm not advocating welfare or abuses of the system, but the blame shouldn't be on the people, but with the flawed system that enables those to abuse it by paying more than most jobs. Any fix to the system will only hurt the people and kids that truly need the help. So it's a lose/lose any way you look at it.
Just my 2 cents