Bruce Bartlett talks about who does and doesn't pay federal taxes, and notes that "the growth of the non-income-taxpaying population is largely a result of Republican tax policies."
He also notes that:
There are 78,000 tax filers with incomes of $211,000 to $533,000 who will pay no federal income taxes this year. Even more amazingly, there are 24,000 households with incomes of $533,000 to $2.2 million with zero income tax liability, and 3,000 tax filers with incomes above $2.2 million with the same federal income tax liability as most of those with incomes barely above the poverty level.
But, it is the low income households that Republicans complain about, usually something along the lines of:
Those on the right often complain that it is fundamentally undemocratic for such a large percentage of the population to pay nothing to offset the federal government’s general operations. After all, everyone benefits from national military spending and other federal programs.
But why is it better to, say, tax the poor $100 and then given them $120 in benefits instead of just sending $20? Why go to all the trouble and cost of collecting the extra $100 and then giving it back? Unless the real argument is that there should be no redistribution to the poor, i.e. that they should get back less than the $100 they paid, certainly no more, I don't see why it's better. One argument is that you can earmark the $100 for particular types of spending, but that seems like the kind of paternalism the right likes to (say) they avoid. I guess the argument is that somehow this makes people aware of the value of what they receive, but it seems like a weak argument to me.
In any case, this is hard to disagree with:
Perhaps the right and left can at least agree that it is unseemly for those in the top 1 percent of income distribution, with incomes at least 10 times the median income, to pay no federal income taxes. It’s not socialism to ask them to pay something.
It's also reasonable to ask those at the top to pay their fair share, and to participate in the burden of reducing the long-term deficit through tax increases.
[Update: I should have also pointed to Misconceptions and Realities About Who Pays Taxes.]