The government is to create an environment in which the economy can thrive.
The government is part of the economy; you can't easily separate the two. The government is more than capable of creating jobs both directly and indirectly, but such a method of creation is not the most ideal method of making jobs when other methods are readily available, and such jobs are often inferior to non-governmental jobs.
The average person does not understand that the minimum wage is not an optimally efficient or especially efficacious1 policy option, but one that is generally, though not always, better than no policy to the extent that it has an impact. In fact, the positives and negatives of the minimum wage tend to be vastly overstated by both sides.
1At combatting poverty or cost of living. There are better solutions to both than the minimum wage that also address efficiency.