Can someone explain how the Republicans can cut taxes and reduce the National Debt?

Obama or Nader asked: The Reagan, Bush, and Bush Presidencies have clearly demonstrated that trickle down economics balloon the National Debt. Why do Republican candidates still call for tax reductions which will create more debt and reduce the value of the dollar?

http://www.lafn.org/politics/gvdc/Natl_Debt_Chart.html

Racist Pig – That simply isn’t true.
Locutus1- That’s a great theory, but [...]