The interesting part of that statement is the word "back" and the implications it has. At first glance Biden is just playing Robin Hood, taking money from the rich and giving it to the poor (who they refer to as the middle-class). If that was the case then he would have phrased it differently.
By using the word "back", Biden implies that the rich somehow have money that they took from the poor and it is the government's job to give it back. How does he come by that notion?
Democrats have been insisting that Bush's tax cuts were unfair because they favored the rich. This can be argued either way but the important thing here is that Bush did not raise taxes on the poor (or middle-class). He lowered them. No money was taken from the poor.
Maybe Biden means that Obama will take the tax cuts that should have gone to the poor (middle-class, whatever) and give them where they belong. But that isn't what he said, either.
I suspect that Biden's statement comes from a socialist zero-sum view of economics. If someone is rich, it is because he took advantage of the poor. This view matches Biden's statement. The rich were allowed to make too much money so it is up to the government to redistribute some of it from the undeserving rich to the deserving poor (they deserve it because simply they are poor). This fails economics 101. If I sell you something I may make a profit but that doesn't mean that I took advantage of you. You were free to not buy from me (there are exceptions to this but most involve government-sanctioned monopolies). You gained something of value to yourself.
There have been hints before that Obama was influenced by Marxism. Apparently Biden has a similar background. The idea of government redistribution of income seems like classic Marxism.
A side-note to this. Rep. Chris van Hollen (D-md) tried to justify Biden's statement this way:
This is disingenuous. Biden was not suggesting that the rich pay more taxes in order to support the troops or even to lower the deficit. He (and Obama) want to give the money from the new taxes to the poor. If Obama and Biden were suggesting an across-the-board tax hike with the rich paying most of it then Biden might have a point. This is nothing of the sort.
Look, as Barack Obama himself has said, and as we all know, nobody likes to pay taxes. But I would ask Governor Palin a simple question; How do think we're providing equipment to our troops in the field in Iraq and Afghanistan? How do you think we're supporting the wounded veterans who are coming home at places like Walter Reed and other military hospitals? How are we supporting our troops in Afghanistan?
I thought it was patriotic for all of us to be supporting the troops in the field and providing them with the resources...
A second side-note. The Democrats love to point out that McCain was against Bush's tax cuts but wants to keep them. They say that this represents a flip-flop. It does not. McCain voted against the tax cuts in protest because he wanted matching budget cuts. Regardless, he has pointed out that rolling back tax cuts years after they passed amounts to a tax increase which he also opposes.
Maybe this is too nuanced for the democrats.