Should Americans who don't pay any taxes be allowed to vote?

According to the IRS roughly 48% of Americans do not pay any federal income taxes. There was a statement I read where it was said that our democracy will collapse when portion of the voters who do not produce anything realize they can vote themselves income from those of us that produces. With the federal government on the verge of bailing out numerous industries who will eventually have to pay for this ...is this the beginning of our demise. Should those who do not contribute to the US economic pie be allowed to vote and shape decision about our economy