The problem is simple: The 47% are Romney's most loyal supporters. Let's look at them in detail.
The elderly and disabled: 61.6 million, about 21% of the population. These are Romney's most loyal suppporters. However, even my mother, who is in her mid-80s and depends on her social security and VA checks to live, thought twice about voting for Romney after those remarks. Speaking of the VA, a lot of those disabled people who pay no taxes are veterans, another core republican constituency.
The unemployed: The U6 unemployment rate is now 15%. In 2000 it was 7%. Unfortunately for Romney, most of these people are steadfast republicans who blame Obama for the fact that they lost their jobs, their homes, and their ability to pay taxes.
The working poor: 7.2% of the population. The problem is that the poorly educated, working poor are also consistently republican voters. They consistently vote against their own economic self-interests due to opposition to democratic positions on abortion, gay rights, and other social issues. While they don't pay income taxes as such, they often pay as much as 30% to 40% of their income in total taxes, depending on the state, in the form of state taxes, sales taxes, user fees, tag and title fees, personal property taxes, etc.
Then there is the half of 1% of the population who are in the top 1% of wage earners who pay no income taxes due to the intricacies of the tax law.
The religious leaders: These are less than 1% of the population but they have a huge voice in the elections. Preachers, priests, missionaries, nuns, etc. pay no taxes due to non-profit status and vows of poverty but they make their opinions known to the 41% of us who attend church every Sunday, according to Gallup polls, and they are almost universally republican, primarily due to the Democratic stand on abortion. .Assuming that the 41% who attend church on any given sunday aren't always the same 41%, it's probably a safe bet that something on the order of 75% of the population will hear their opinions over the course of the election cycle.
Finally, according to the CATO institute, a republican think tank, 4.1% of the population are on welfare. However, even this group isn't in the democrats' corner, as the poorest 5% of the population don't vote very often.
And that leads to the underlying problem: While Romney can rely on winning the vast majority of the "47%"'s vote, it's the other 53%, who pay all the taxes, that will vote for Obama. The well-educated professionals who pay most of the income taxes, the middle-class females, and most of the other high-earning groups are more likely to vote democratic.
The republican party has forgotten who their core constituency is. If they want to win elections, they need to quit vilifying the very people who keep voting them into office.