As it turns out, the United States’ federal government shutdown is not without precedent. In 1975, Australia experienced a similar shutdown after its legislature became embroiled in a deadlocked squabble about the country's budget.
While the U.S. shutdown has yet to be resolved, it is highly unlikely that Congress has much to learn by following Australia’s example.
After the 1975 shutdown, Sir John Kerr, Queen Elizabeth II's official representative in Australia, dismissed and replaced then Prime Minister Gough Whitlam. A new bill that authorized funding for the government was passed almost immediately. Then, Kerr proceeded to dismiss the entire Australian Parliament.
Though at the time the methods were deemed unorthodox, history has proven them successful. Case in point: Australia has not had another government shutdown since.
Note: This entry has been updated to indicate that Queen Elizabeth II did not order Kerr to dismiss the Prime Minister. In fact, reports suggest she was not consulted on the decision.