They both took/take over a country that was/is severely politically divided. In Lincoln's case, it was the pro-slavery versus anti-slavery political ideals. For Obama, it's the conservative versus liberal political ideals.
Also, Lincoln sought to put together a cabinet of his political enemies. His point was that he didn't want to get caught up in a kind of groupthink (like the Bush administration admittedly did in the run up to the Iraq war). Once when George HW Bush was asked why he would choose a VP with whom he often disagreed (Mondale), he replied that he didn't want a VP who agreed with everything he thought, because then you only have one person thinking. But, if they disagree, then you have two people thinking.
That's basically what Obama is trying to do with the appointments he's making to his cabinet. And, even Rush Limbaugh is impressed (go figure).