http://languagelog.ldc.upenn.edu/nll/?p=2
Donald Trump rally 12/21/2015, Grand Rapids, Michigan:
l- let me just tell you
I may win, I may not win
Hillary
that's not a president
that's not- she's not taking us to the-
everything that's been involved in Hillary has been losses you take a look
even her race to Obama
she was going to beat Obama
I don't know who'd be worse
I don't know
how does it get worse?
but she was going to beat- she was favored to win
and she got … schlonged, she lost, I mean she lost
Mr. Trump's choice of terminology caused a certain amount of discussion, so he replied:
When I said that Hillary Clinton got schlonged by Obama, it meant got beaten badly. The media knows this. Often used word in politics!
— Donald J. Trump (@realDonaldTrump) December 23, 2015
One result has been more linguistic analysis in the non-linguistic media than we've seen in a long time.
Justin Wm. Moyer ("Donald Trump's 'schlonged': A linguistic investigation", Washington Post 12/22/2016) recruited some expert analysis:
In an email to The Washington Post, Harvard University’s Steven Pinker, a noted researcher on language and cognition, pointed out that Trump, using a term that comes to English via Yiddish and Middle High German, may simply have been trying to say something else.
“Given Trump’s history of vulgarity and misogyny, it’s entirely possible that he had created a sexist term for ‘defeat’ (as far as I know there is no such slang verb in Yiddish),” Pinker wrote. “But given his history with sloppy language it’s also possible that it’s a malaprop.”
Trump’s problem? He’s a gentile who, linguistically, may have wandered too far from home.
“Many goyim are confused by the large number of Yiddish terms beginning with ‘schl’ or ‘schm’ (schlemiel, schlemazzle, schmeggegge, schlub, schlock, schlep, schmutz, schnook), and use them incorrectly or interchangeably,” he wrote. “And headline writers often ransack the language for onomatopoeic synonyms for ‘defeat’ such as drub, whomp, thump, wallop, whack, trounce, clobber, smash, trample, and Obama’s own favorite, shellac (which in fact sounds a bit like schlong). So an alternative explanation is that Trump reached for what he thought was a Yinglish word for ‘beat’ and inadvertently coined an obscene one.”
Over at Talking Points Memo, Josh Marshall engaged in 3,000 words of ethnographic investigation ("The 'Schlong' Revisionist Analysis We've Been Waiting For?", 12/23/2015; "Trump Doubles Down on "Schlong", New Truth Movement Emerges", 12/23/2015):
Since our initial post we have had a number of TPM Readers (generally men born between 1940 and 1952 in Queens and Long Island) who have clear testimony about what we might call the "Trump/Schlong" usage (aging Jewish male readership finally comes in handy!).
For instance, TPM Reader BR explains the following …
I also grew up on Long Island at the same time as Trump (born in 1949). I too remember "got shlonged" as a common expression (usually in sports) with no sexual overtone. My only criticism of Trump's usage would be that in my recollection the term applies to a team, not an individual. "We got shlonged" sounds right, "I got shlonged" totally wrong. "He got shlonged" doesn't seem as right as "they got shlonged," but the difference isn't as clear-cut to me.
I also think that the everyone probably has the etymology wrong. The more likely etymology is from Yiddish & German schlingen, meaning to devour food. (I know the verb from the Yiddish song "Un az der rebbe zingt" with "Un az der rebbe esst, shlingn alle khasidim," although the version I see on the internet is different.) The simple past tense of this word in German (that tense doesn't exist in Yiddish) is schlang.
So not only did Trump not make the word up, not only is it not vulgar, but it may not even come from Yiddish.
[…]
It seems clear to me – based on BR's testimony and ones from at least half a dozen other people – that in the 1950s in Queens and the near-adjoining parts of Long Island "schlonged" was a known phrase, often used in sports references, and at least from the youthful memories of our witnesses could be used without the users having a strong conscious sense of any sexual meaning behind it. The frequency with which it is remembered as being mainly a sports metaphor is notable. […]
At the same time, from emails, Facebook discussions and other sources I've seen numerous Jews, people with deep familiarity with Yiddish, saying they have never, ever heard the phrase used in this way.
We have another account from TPM Reader BD who grew up in this general area in the 60s and 70s, in other words a good ten to twenty years after the putative Queens/Long Island schlong era.
I grew up on Long Island too, 20 minutes from the Queens border. I’m not Jewish but between friends and my father, who was a former shabbos goy, I've heard and used Yiddish all my life. Schlong has, in LI/Queens usage, no meaning other than penis. I don’t really remember hearing the verb schlonged much if at all, but even if it was commonly used the connection to penis is unmistakable. Yes, it would be a milder way of saying “fucked."
And Barbara Morrill at Daily Kos does some OED-style historical lexicography ("Donald Trump says 'schlonged' is an 'often used word in politics' … is he right?", 12/23/2015):
[A] Nexis search of the word “schlonged,” from 1990 through December 20, 2015, turns up a number of instances of the use of the word. Five, to be exact.
There was a 2007 episode of The Man Show where, during a segment on pornography, there was a deep discussion about “spunk,” “neanderthal women pleasuring the wooly mammoth,” “delightful vaginas of yesteryear,” along with their “donkey-schlonged male counterparts” (which are apparently “angry, purple and veiny”).
There was a 2010 review of an undoubtedly charming cable TV show called Hung, that followed the adventures of a “formidably schlonged sports coach.”
Then there was a 2011 episode of NPR’s now-defunct Talk of the Nation, where host Neal Conan, speaking on the death of Geraldine Ferraro, noted that she was the first woman to run for vice president on a major party ticket, but “that ticket went on to get schlonged at the polls.”
In a 2014 article about the death of Phillip Seymour Hoffman, his role in Boogie Nights, where he played a “gauche gay boom operator with a crush on long-schlonged superstar, Dirk Diggler” was cited.
And finally, there’s a 2014 gossip column talking about a participant in a British reality TV show who was described as “pint-sized and long-schlonged.”
So there you have it. It’s just an often used, common political expression … assuming you’re discussing the size of a candidate’s penis or a woman losing an election to a man.
You can extend the lexicographical investigation yourself, via Google Books or other resources. Meanwhile, Donald Trump has dominated the Christmas news cycle without spending a penny on publicity:

Update — I somehow managed to miss Ben Zimmer's contribution to schlongology, "The Full History of Political 'Schlongings'", Politico 12/22/2015:
While the expression is rare, it has in fact shown up in earlier political contexts, typically from New Yorkers like Trump. The Post notes that Neal Conan, host of NPR’s Talk of the Nation, said in a 2011 broadcast that the 1984 Democratic ticket of Walter Mondale and Geraldine Ferraro “went on to get schlonged at the polls.” And on Fox News in 2006, Dick Morris warned that President George W. Bush was “going to get schlonged” in the midterm elections.
Long before that, the phrase made an appearance in New York City collegiate politics. The Daily Mail uncovered a 1967 article in the student newspaper of the City College of New York in which Ellen Turkish, a candidate on the losing slate for student council, said, “We got schlonged.” (As Ellen T. Comisso, she would go on to a distinguished career as a political scientist.)
[…]
Will Trump suffer any long-term political fallout over “schlong-gate”? His polling numbers do not seem affected even by his most outrageous statements, so his latest choice of words likely won’t matter, at least in the short term. But over time, his vulgarisms may paint him as rhetorically unpresidential, and he could be the one getting schlonged in the polls.
In any case I think we can guaranteed an uptick in schlong sightings — for example, Brad Delong's 12/23/2015 series of tweets on why "The Federal Reserve's 2%/Year Inflation Target Was a Mistake", which being concatenated read:
Back at Jackson Hole in 1992, LHS’s and my point that an inflation target much less than 5%/year had the strong drawback of making it likely that we would have nasty experiences at the zero lower bound was countered. It was countered by people saying that even if adverse shocks did drive the Fed to the ZLB sometime, such excursions to the ZLB would be rare and short. Confidence in the durability of the “Great Moderation”, and the consequent belief that we did not need to worry about what might happen in what @ojblanchard1 calls “dark corners” was, in retrospect—and some of us thought in prospect—very wrong. It was, I think, a major element in what led the economics department to put itself in a position where it got itself schlonged by reality since 2005 or so…