The logic is that high taxes discourage these guys from working, and low taxes lure them to work harder to get even richer. Since these folks already have all the money they could possibly need, so their primary motivator must be greed.
Other tenets of the conservative orthodoxy are that even the poorest people should be forced to pay taxes to make them feel "vested," that they don't need the payroll tax cut President Obama instituted, that the minimum wage should be eliminated and that unemployment and welfare benefits are inherently evil. Even Medicare and Social Security should be abolished in the long run.
The logic is that the more money these lazy poor people have, the less inclined they will be to work. That is, their primary motivator must be need.
Corporate profits have been up in the last few years and many companies are just sitting on tons of cash. Tax rates are down significantly from what they were 15 years ago (halved on capital gains!). That was the last time our economy was doing really well, and people at all income levels were doing better.
The fact is, dozens of large corporations already pay no taxes at all and hundreds pay very little. Lowering their taxes will provide no additional motivation. But corporations are not creating lots of jobs in the United States, even though they could easily afford to. Why?
They don't need to. CEOs are swimming in corporate profits and getting bonuses out the wazoo. It's easier for them to sit on their duffs, make their current employees work more hours, offshore more jobs, and take no risks.
As a motivator, need trumps greed every time. By conservative logic, since greed is failing as a motivator we must enlist need. In other words, the laziness and overweening sense of entitlement that conservatives insist permeates the lower classes has become even more pervasive in the upper crust "job creators," and should be slapped down with equal force.
The obvious answer? Raise taxes on "job creators" unless they actually create jobs. In particular, companies that funnel jobs and profits overseas to escape US taxes should be hammered. That will make them work harder, the same way cutting off welfare and unemployment benefits forces the poor to work harder. To maintain profit margins the CEOs will have to expand their businesses and create more jobs. And if they're like Ayn Rand's ostensible heroes and just take their ball and go home? Corporate shareholders will just replace them, or ambitious newcomers will rise up to do the job they're too lazy to do.
There's plenty of evidence that higher taxes (within reason) don't hurt the economy. The US economy performed much better from the 1950s through the 1990s when taxes were higher (much higher in the 50s) than after the Bush tax cuts. As Paul Krugman points out, high-tax Sweden and Austria are doing better today than the United States and the rest of Europe.
With more people earning more money, there will be more customers for those companies, which will mean more profits.
Thus, satisfying need and greed at the same time.