The world record for a democracy going without an elected government is held by Belgium, which went 589 days in 2010-11 because the opposing Flemish and Walloons were unable to agree on policy issues and form a governing coalition following national elections.
But day-to-day affairs of the country were tended to by a temporary government run by a former prime minister, while the two main political parties fought over everything “from Flemish collaboration during the Second World War to allegations of francophone cultural imperialism seeking to impose the Gallic language in Flanders,” according to this 2011 article in The Telegraph. The divisions are so deep that many people expect Belgium to split into two separate countries at some point.
The temporary government did not make big decisions regarding budget (though money still flowed as before), the national debt, foreign policy and defense, leading some to worry that a debt crisis could occur and affect all of Europe. It didn’t happen.
The consequences of the U.S. government shutdown, which started Tuesday, could be different, depending on how long it lasts and whether Congress decides to retroactively pay the 800,000 federal government workers who have been furloughed.
Maybe we need a caretaker Congress until the elected one can sort out its mess.
Incidentally, Belgium took the dubious distinction of going the longest time without an elected government from Iraq after the fall of Saddam Hussein.