What does ‘Democratic sharpies’ mean? Is the usage of ‘sharpie’ as a political figure well-received?

Given the context, I'm assuming that it's referring to a sharp person. I think the word pundit could be a workable substitution.

Incidentally, when I was looking around in various dictionaries, I found this is NOAD:

I thought that was worth a mention, because you said:

none of dictionaries I’ve checked registers ‘sharpie’ in political connotation.

(Several people I know would find a direct link between a "dishonest and cunning person" and politics). That said, I don't think the Time reporter is making that inference; I think Helperin is referring to political strategists – not necessarily hard-liners – as "sharpies."

As for your second-to-last question (“Is ‘sharpie’ a received English word?”), I think it is indeed acceptable; the Time article would attest to that. That said, it's not commonly used in that context, and most in the USA would probably think of permanent markers before they associated the word with keenly intelligent wonks.

It has no political connotation that I'm aware of. In your example, it's simply being used in its sense of "exceptionally keen or alert person" as you noted.