The chart above reflects the results of a recent Rasmussen Poll -- done on September 4th and 5th of a random national sample of 1,000 likely voters, with a 3 point margin of error. It shows that 45% of Americans believe tax cuts help the economy, while 55% either believe they don't or are unsure as to whether they do or not.
Who is right? Well, the "unsure" people are right -- because this question can't be answered without knowing who is going to get the tax cuts.
If the rich get the bulk (or all) of the tax cuts, then the economy will not be helped. These people already have the money to buy anything they want, and giving them more will not increase the amount they buy. It will just fatten their bank accounts, and even if they did buy more, there aren't enough of them to significantly affect the national economy.
If the tax cuts go to the working and middle classes, then the answer is Yes. The economy will be stimulated (rising demand and creating jobs) because they comprise many millions of people -- and when they spend more, the economy is spurred and demand is increased.
Tax cuts might or might not help the economy. It all depends on who gets the cuts.