Free ride can also include enjoying all that America has to offer without contributing to the tax base.
Single mom example falls on the deadbeat dad not providing for his family. It’s a sad situation usually created by either ****** people (deadbeat dads) or ****** decisions. And the government offers assistance for this in the form of handouts, which for this narrow use case, I support (when paired with aggressive pursuit of dad’s wages to offset expense).
The very first federal income tax ever levied in the United States excluded lower incomes. This "skin in the game" concept you're perpetuating has never been a part of our federal income tax. So, what you're proposing is a complete reimagining of what has been the American federal income tax, and the justifications behind it.
As to your commentary re single moms, you're showing your bias here a bit ... and your underlying vindictiveness ... perhaps she's a single mom because the dad isn't a deadbeat, but, instead ... he's just dead? Or maybe she's the victim of rape? Or some other circumstance which doesn't necessarily "demand" besmirching or belittling someone? And I would guess your bias wouldn't end there ... it would make you less willing or unable to sympathize or empathize with a good number of cases that result in need, or having less than might be necessary to survive.
It probably also sheds some light on the reasons behind your desire to implement this "skin in the game" aspect to the federal income tax. The "free ride" characterization would tend to support these reasons, as well. It's more a "punishment" to get your way, than anything else. So, at which level of taxation should these folks currently not paying federal income tax be taxed? And, what do you think this will accomplish, practically speaking?
So, this guy/girl/family who is having trouble making ends meet, or can't make ends meet, suddenly has to give X% of their income to the federal government ... now what? Are you hoping this spurs them on to vote against taxes, generally, or against raising taxes? Are you hoping this alleviates tax burden on those in a better position to pay it? Or, do you just want to see them suffer more, and not get that free ride? If they're having trouble making ends meet, and they're getting government assistance ... and now they have to pay more .. that will mean they need even more government assistance ... so what did that change about anything?