Scum itself has been used for many hundreds of years to refer to offensive, disgusting, or disreputable people, and thus many people take scumbag as an intensification of this scum with the suffix -bag, a frequent element in abusive slang terms (dirtbag; hosebag; sleazebag; etc.), all of which are, however, later than scumbag.
Though most people seem not to realize it now, the original sense of scumbag was 'a condom', based on the slightly earlier, and both rather obvious, scum 'semen' and bag 'a condom'.
People's reaction to scumbag today tend to reflect their awareness of the 'condom' sense, with those who are aware of it finding scumbag significanly more offensive than those who are not. While certainly offensive, scumbag is not in the top tier of the most offensive terms in English. It is more offensive than jerk or creep, but less offensive than, say, asshole. But to publicly call an elected official a scumbag still seems a fairly extreme step, even given the current state of political discourse in America. Note that the New York Times, often squeamish about such matters, did not print the word and used a euphemism instead.
Though most sources claim that both senses, 'condom' and 'disreputable person', date from the late 1960s, the first sense is found in underground literature at least by the 1930s, and the second by 1950.