It really depends on the current level of taxation and the kind of tax you’re talking about to determine how rapidly cutting it will pay for itself. Income taxes, capital gains taxes, sales taxes, corporate taxes and sin taxes all have differing impacts on the economy; and you will get different results from cutting each of these taxes. At the same time, when tax rates are low it is unlikely that you will see as significant or rapid of tax revenue increases from cutting the tax rate as you would if the tax rate is high.
Ultimately, there is another important factor which American politicians do not seem to understand. You have to cut spending proportionately to tax cuts initially because the debt that is created will have interest payments which could eliminate the benefit of your tax cuts.
