Anyway: we're at a point at which even Jonathan Chait, writing against panic, says that "the current sense of dread enveloping the Democratic Party has a very real basis. President Obama’s poll numbers are plunging to unprecedented depths."
Yes, it's all massively overstated.
Plunging? His approval (and some associated numbers) have definitely dropped. I suppose "plunge" is subjective, but HuffPollster's estimate, set for "less smoothing" and therefore (over?) sensitive to recent polls, is that he's lost maybe 2.5 percentage points over the last five or so weeks. He's been losing ground all year including, mostly likely, during the shutdown. Depending on what adjustments one does, that might have accelerated after the shutdown, or maybe not. It doesn't sound like a "plunge" to me.
Obama's popularity is probably at the low point of his presidency (again, depending on the adjustments, he's either a bit below or a bit above his previous low. But it's not any kind of unusually low low point (he's nowhere near Truman, Carter, Nixon, W.), there's no particular reason to expect the slump to continue, and myths aside no reason to believe he won't recover if the news turns better. Granted, it's hard to know what to expect from healthcare.gov, but it's not as if it's getting worse over time. I'm not saying his numbers will go up. Just that it's more or less equally likely as further drops.
(Actually...if I had to guess, I'd say a run of either stability or improvement is probably more likely, at least if the next budget deadlines come and go quietly. Gallup's economic confidence index has been steadily recovering from its shutdown/debt limit plunge -- yes, that one was a real plunge -- and Jamelle Bouie is right that the economy is a very big part of presidential approval, although I think he somewhat understates the ability of other events to matter).
As for electoral effects? I wrote an item dismissing direct electoral effects of the shutdown against Republicans back last month; that post pretty much works now, in reverse for effects against Democrats. I should say: it's far easier for sentiment against the president to translate into midterm electoral losses than it is for feelings against the out-party. So if Obama is unpopular in November 2014, it will hurt Democrats. But today's frenzy about the ACA is going to be mostly forgotten by then, one way or another, just as the shutdown seems forgotten today. That's probably even true, believe it or not, if the program totally collapses, although I don't think that's going to happen.
Anyway, Obama's approval ratings have in fact fallen from the mid-40s to the low-40s, and over the course of the year from around 50 to the low 40s. It's obviously not good news for him, but it seems a lot less dramatic than a lot of the chatter this week would have it be.