A tax cut in a recession will help in recovery, and hence reduce the deficit.
A tax cut in recovery will simply increase the deficit.
That is why Alan Greenspan said that "Tax cuts don't pay for themselves". So much for silly answerers here.
A tax cut will always, and has always reduced the trend rate of tax revenue.
A tax increase has always, and will always increase the trend rate of tax revenue.
The pubs here confuse the automatic increase in tax revenue due to other factors such as increase in inflation, population, economic output with the effect of a tax cut. It has been studied by economists and not only is there no logic to the idea, it has no empirical merit as well.
So, to answer your question, the reason why Republicans call for tax cuts and complain about the deficit is because they don't know anything about economics. Instead of going to Beck rallies about restoring honor, they should simply take an economics class.