Is “Not to generalize or anything” an idiomatic parenthesis?
Solution 1:
Normally, not to x or anything is followed by a but, like this:
Not to generalise, but women often spend too much on shoes they never wear.
Here, it is short for [I do/did] not [mean] to generalise, but... It is a caveat, and a warning that what you are about to do (or have just done) may be interpreted in a bad way.
In casual speech, or anything is often tacked on to make the generalisation seem less explicit, less important, as in: "I may be generalising here, or I may be doing something else—it doesn't matter anyway—, but...".
Using not to x or anything without a following but looks like sloppy writing to me for a serious article, which is probably part of the reason why it confused you: the generalising statement ought to follow, explaining the caveat—but no such statement follows here, at least not immediately. It is not a grave sin, but it's not exactly eloquent here. Most writers would only use that in a very casual context.
Based on the rest of the article, I believe the generalisation is supposed to be the writer's theory that "[m]ore recently, however, Romney’s luck has turned", as mentioned at the start of the paragraph. The statement by Romney about the 47 % is supposed to be an example supporting the theory. But at the same time it is probably a sarcastic quip referring to Romney's own generalisations in these quotations.
The this that comes immediately after is unrelated to the not to generalise: it refers to the 47 % statement, the example supporting the theory. It is short for something like this [was/happened], or [and notice how] this [was]. It is meant to make clear that there is a connection between the previous example and what follows, Romney's statement about Obama.