The BBC provides this explanation and definition of the term:
The vast majority of parliamentarians do not hold ministerial or shadow ministerial office and are known as backbenchers. They are so-called because they sit on the back benches of the Commons or Lords – ministers and their opposition counterparts sit on the front benches.
The OED cites a first British use in 1910, and more than a century later it’s unavoidable in the U.K. and other countries with a Parliamentary system. But it took a long time for Americans to start to use the the term to refer to their own politicos. The moment finally arrived in in 1988 (at least in the archives of the New York Times), and the person who used it was none other than Representative Newt Gingrich, who had filed ethics charges against Speaker of the House Jim Wright. Gingrich (whose fondness for another Britishism has been covered on this blog) was quoted in the Times as saying: ”If Jim Wright were a backbench member, I probably wouldn’t have done anything…. But he’s the Speaker, and everything he could have done all his life as a backbencher becomes self-destructive when he becomes third in line to be President of the United States.”
The first time a Times reporter called an American a backbencher was four years later. Now it’s a commonplace. Four of the last six times the term’s been used in the Times have been in reference to Americans, most recently a January, 5, 2013, Ross Douthat column in which he noted that Speaker John Boehner’s “own backbenchers blew up his attempt at a fiscal cliff negotiating maneuver.”
It’s a useful term, but it bit less potent than in the U.K. since here, it’s not only metaphorical but untrue: since 1913, members of the U.S. House of Representatives have been allowed to sit anywhere they want.
notoneoffbritishisms.com 
It would be more impressive as a NOOB were there U.S. references in multiple sources beyond the “elite” NY Times.
Et tu, Hal? How about this:
“At a meeting on ethics reform this month, State Sen. Josh McKoon reflected on the advice he was given two years ago when he entered the Senate.
“Sit down, shut up and listen,” he said.
“Instead of taking a backbencher’s traditional role, Mc-Koon agitated in his own party for ethics reform, a politically tricky maneuver even for a veteran legislator. And while it did not endear him to his caucus, McKoon’s retelling drew a chuckle from Democratic leader Sen. Steve Henson, D-Tucker, an ethics ally who sat next to McKoon at the event.”
Atlanta Journal-Constitution, December 25, 2012
Ben:
I have no brief against using backbencher in a metaphorical sense in the US, despite its genesis from a seating arrangments in Commons; in fact, it works rather well as a grab bag, allowing the inclusion of “freshmen,” “newly-minted members of Congress,” and various descriptive circumlocutions, some of which are perhaps justifiably scatalogical in nature.
However, it could confuse some who might conflate “backbencher” with “on the bench,” as in a judge, or a substitute in a ball game.
I was about to say that backbencher is a more useful term in parliamentary systems, where some parliamentarians also hold ministerial positions. But then it occured to me (and correct me if I’m wrong) that US legislatures have powerful committee systems. So in the US, a backbencher would be a parliamentarian (don’t know what the universal US term is off-hand: legislator?) who aren’t on these committees, or perhaps even better, those who are not chairs.
I suppose it is possible for confusion to arise, but then the same people would probably be confused by my use of “chairs”, instead of chairmen/women/persons. Hmmm.. discussions of the legislature and judiciary seem to use an awful lot of furniture terms (and see also Chancellor of the Exchequer).
In a Westminster system, the difference between “government backbencher” and “minister” is much more significant than between “opposition backbencher” and “opposition (front bench) spokesperson”. This is doubly so in a small or multi-party parliament; Ireland’s is both, and the two main opposition parties have so few representatives that almost all of them are spokesperson for something or other.
Now, when you say “the Times”?
The American paper is the Times, the British one The Times.
We, and the Times, seem obliged to say “the Times of London” now, it seems?