To test whether reducing corporate income taxes will spur economic growth and reduce government debt, just apply a thought experiment at the extremes: compare what would happen if the income tax were 100% with 0%. At 100% income tax, corporations would have no reason to employ anyone, so the unemployment rate would go up. The unemployed people would be a cost to the government, increasing government debt. At 0% income tax, corporations would hire more because each worker's net contribution would directly increase profit. More employment reduces government costs, increases government revenue, and reduces government debt.

So it seems that the argument that decreasing income tax rates would not decrease government debt is the laughable argument. It at least doesn't work at the extremes.