Being rich is having enough capital to escape the trap of wage slavery that is a 9-to-5. It is really hard to fathom the idea of money working for you instead of you working for money when $15/hour sounds like a lot of money though so I understand where "a lot of people" are coming from. However, raising the highest marginal income tax rates isn't raising taxes on the rich. It is raising taxes on the upper middle class - the most highly paid of the wage slaves.
The Micawber principle (from David Copperfield) comes to mind here: "Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds nought and six, result misery." 20 shillings to a pound, 12 pence to a shilling, so the difference between happiness and misery is a single shilling (or 1/20 of a pound).
Remember hearing Dave Ramsey (who probably got it from someone else) saying that when your money makes more than you do, you're officialy rich. There might be something to it.
If you've got some 9-to-5 job pulling down $80k/yr with no kids or dependencies, you're rich to a lot of people.