Jonathan Cohn argues why he likes the term "Obamacare":

As you may have noticed, opponents of law love to use it and supporters don't. And it's safe to assume those opponents don't mean it as a compliment.
It's not just that they want to tie the law, which they hate, to President Obama. It's that they want to reinforce the idea that it's something Obama, and the Democrats, crammed down the throats of the American people....
I like the term. I think this bill will be popular someday and, in the meantime, I think it's a reminder that this administration did something that will help millions of Americans while starting to put our health care system in order. Maybe I'm wrong--I've certainly been wrong about this before--but I think that within a few years, and maybe even by 2012, association with the health care plan will be a net plus.
In fact, my only objection to the term is that it's not entirely accurate. 

Well, accuracy is the hang-up -- and, being a journalist, I want to use the most accurate term. We don't call Medicare "Johnsoncare," though it would have been to the Democrats' long-term advantage to do so. I think "Obamacare" works to help Republicans define the Affordable Care Act as a partisan hate object. I suspect they also thought, or still think, that it would bring down the measure's popularity. But of course, they're identifying it with a president who's fairly popular and  more popular than either the Republicans in Congress or the Republicans who plan to run against him in 2012:

Poll
Obama Favor. GOP Favor. Obama Unfavor. GOP Unfavor.
CBS/NYT 49 40 39 49
NBC/WSJ 52 51 32 40
Gallup 49 47 42 43

So calling it "Obamacare" is pretty good branding. Still, I think accuracy argues for using the law's real name.