The word was first coined by Malcolm Tucker (Peter Capaldi) in the last series of the sitcom to describe then-government MP Nicola Murray (Rebecca Front) on learning that she was claustrophobic.
Labour Party leader Miliband borrowed the phrase in the House of Commons to refer to George Osborne's "omnishambles Budget" earlier this year, and it gained further traction in Parliament and the political press.
"It feels like politicians are watching the show and embracing it," show co-writer Smith told ShortList.
"Ed Miliband used the phrase 'omnishambles'. That was baffling. It wasn't particularly flattering, it was more like, 'What the hell are you doing?'."
After Miliband's comments in the House in April, show creator Armando Iannucci quipped on Twitter: "Fantastic. With the royalties from Miliband's 'omnishambles' quote we've now secured enough funding for a new series."
Producer Adam Tandy has said that the upcoming series of The Thick of It will have less swearing than previous years as the incoming coalition are "more prim".
Watch the original 'omnishambles' scene from The Thick of It below: (WARNING: ADULT CONTENT)