As Brad Plumer explains on Ezra Klein's blog, only "6.9 percent of households ... are non-elderly and have incomes less than $20,000 per year and aren’t paying the payroll tax .... [and thus] pay neither income taxes nor payroll taxes."
That's a far cry from 47 percent. What's more, this group votes with much lower frequency than the members of more affluent households. So even if one otherwise accepted Romney's "moocher class" theory, we're talking less than 5 percent of this November's likely voters, not 47 percent.
I think what's coming out here is the anger of someone who doesn't feel he should have to ask people for their votes, just as he feels he doesn't owe them any disclosure of his finances or of what policies he would follow. Contempt for the public, for democratic institutions, and for all people who disagree with him or offer insufficient deference is not a good basis for establishing trust.