I know what you mean. It's Darrell Hammond's definition of a successful impression.
In Jay's case, he doesn't know how to dial down his energy and play an impression subtle. You could chain Darrell hand and foot and put him in a mask that covered everything but his mouth, and he could still do Cheney just with the crooked smirk.
At a minimum, to do Obama you have to be able to play his cool demeanor and faultless diction. Most people can't even do that. I've had professional voice training and I cannot match Obama's precise enunciation without concentrating. Physically, he's so centered and relaxed. He doesn't have any hitches or "tells" that you can accentuate for a laugh.
If anyone ever comes up with a truly funny Obama impression, I think it'll be based on the dialogue, not on the physicality.
Still, Armisen's Obama is mostly terrible because he sounds nothing remotely like him. And most impressions have at least some of the humor come from the fact that they are sounding like the person impersonated (obviously SNL has shown an few exeptions). And Jay does have the voice and mannerisms down. At least if someone had that figured out for once we could forget about that and focus on the dialogue in the sketch. But there's nothing wrong at least improving in that direction even if it doesn't perfect it. Seriously enough with Armisen! Lorne, for crying out loud how can you keep an impression this bad for so long?!
As far as whether Obama can made fun of well, I absolutely think that's possible. Its not that difficult to make fun of him. His unnatural obsession for perfection in public is ripe for humor and should have been made fun of a long time ago. Every time he's in public its as if every word, movement, and/or glancehas been thought through ahead of time. For a while he couldn't go anywhere or say anything without a teleprompter. This practically screams for something sort of like "Ronald Reagan Mastermind" with a twist. Not to mention his youth and inexperience could have probably been made fun of constantly. If they can make fun of a politician for being old, then why not for being young? They could have had a childplay him in some sketches with him walking around the office wearing a suit that was too big for him. I'm just not sure that anyone wants to make fun of him. I don't think its hard to at all, I just think people are scared to do it. Maybe he's just too controversial? I don't think they're trying hard enough.