Tax cuts would reduce the deficit. Tax cuts always pay for themselves and create more jobs and stimulate the economy. Republicans have said more tax cuts would have been all that was needed to beat the recession and create more jobs in the US. 

While carefully placed tax cuts may or may not eventually pay for themselves, the key word is eventually. The problem is that the finances are so delicate, atm, that "eventually" isn't the solution we need right now.Spending cuts and mild tax hikes on non-elastic taxes (such as a percentage point jump in sales tax) are far more beneficial at this point in time for reining in the deficit.

Once the books are balanced, tax cuts can be played around with more, to see which ones pay for themselves. Though, the idea really shouldn't be about maximising tax revenue, which is essentially what is being suggested here, but should be about reducing the amount of taxes collected, and letting the citizens keep as much of their money as possible.

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.