The video depicting Mitt Romney dissing the 47% should hurt him. People don't want to be called a victim or told they're dependent on the government.
It might not hurt him at all. Half of these people earn too little to pay any taxes. Obama beat McCain 73%-25% with people who earn less than $15,000 per year. Romney could lose some votes in this group, but these people likely aren't voting Republican because of their fiscal policy anyway. If you voted for McCain over abortion, traditional marriage, or the Republican foreign policy you're not jumping ship because Mitt Romney thinks you're a victim.
I'm guessing that many of the remainder fall into a few categories. Some people don't pay Federal income tax but think they do. These people might get Federal income tax deducted from the paycheck and get it refunded April 15. They might think that means they still paid taxes or aren't aware that they got it all back. Others who pay payroll or state taxes assume they are paying Federal income tax.
Some of these people resent the freeloaders without realizing they're one of them.
Romney talked about the culture of dependency where people get Federal help. Some believe they aren't getting it. They might not view Social Security or Medicare as Federal help, since it's their money not the government's. Or they may not consider the money they're getting to be Federal help. They know the welfare mom is the real recipient of all that money.
If people view themselves as victims, then they can't really be that insulted by what Mitt said. Others don't view themselves as a victim even if they have a victim mentality. They do know the other guy, however, is the one with the real victim mentality.
In 2008, Barack Obama famously said that people in Western Pennsylvania were clinging to their guns and religion. In that case, people not only acknowledged that they were clinging to these things, but saw that as a good thing, not a bad one. So it was a diss. Few will think the same about someone who pays no taxes or takes government money.
This should hurt Mitt with the 47%, but many of the ones he has a shot at agree with him.