Is ‘Bash-a-thon’ a received English phrase or just a combination of words?

The latter: it's not a standard word that you'll find in any dictionary. The suffix -athon, as you've guessed, comes from marathon, and means "an event, as a sale or contest, drawn out to unusual length, often until a prearranged goal, as the contribution of a certain amount of money, is reached" (according to Dictionary.com).

One of the joys of language is that words can be manipulated to suit the writer. That 'bash-a-thon' can be understood by the reader is a cause for celebration. By all means one can retreat into standard English for safety, but the hectic joys of neologism shall always beckon. Go forth! Enjoy!

Michael Quinion, Ologies and Isms: Word Beginnings and Endings (2002) offers some additional details about the history of the suffix -athon in English:

-athon After a vowel -thon. An event long in duration, usually for fund-raising purposes. {The last part of marathon, from Marathōn in Greece, the scene of a victory over the Persians in 490 BC.}

From the 1930s onwards, the ending of marathon was borrowed, originally in the US, to form words relating to some charitable activity. The first examples were walkathon, a long-distance walk organized as a fund-raising event, and radiothon, a prolonged radio broadcast by a person or group, similarly to raise money.

Many examples have been created since, of which telethon, a long television programme to raise money for charity, has gone furthest towards general acceptance. Others are operathon, a marathon performance of opera; preachathon, an extended sermon; and swimathon, a sponsored swimming event. Some examples are facetious terms indicating an unreasonably extended happening, such as boreathon, an interminable occasion; plugathon, an extended advertisement for a product or person; and excuseathon, an overextended apology for some mishap.

Newspaper database searches turn up instances of walkathon going back to September 25, 1929, swimathon going back to January 26, 1931, and talkathon going back to February 3, 1933.

The term bash-a-thon also appears in Beth Saulnier, "Saulnier on Cinema: Farewell Double-Header as Miami Blues' Brutal Killer, Alec Baldwin Gets Laughs in the Darkest of Comedies," in the [Poughkeepsie, New York] Miscellany News (April 27, 1990):

And it is here that the film [Miami Blues] takes its strangest, most interesting turn. By this time (meaning after the first fifteen minutes) he has committed enough acts of robbery, killing and brutality to fill up the entire two hours of your average Schwarzenneger bash-a-thon.

In this instance, the bash-a-thon is a typical film consisting of a lengthy series of scripted physical assaults by the action movie star Arnold Schwarzenneger. But in the "Romney bash-a-thon" instance noted in the posted question, the bash-a-thon is a prolonged and perhaps concerted series of verbal attacks by politicians and political commentators on Mitt Romney, presumably for not being sufficiently right-wing. The sense of the term bash-a-thon may thus be fairly literal or it my be figurative. Either way, it certainly does not describe an event performed as a charitable activity.