This view is known as 'underconsumption'. While shown to be logically impossible by J.S. Mill in work published in 1841, if households continually earned money and did not spend it all then leakages from the circular flow could reduce national output and lead to recession.
Of course Keynes imagined a world where people put their savings 'under the bed' and the money literally left circulation. This does not generally happen in the modern world as people leave their money in the bank and the bank ensures that it is not idle.
There are reports of nearly £6 billion of cash being hoarded as people have lost faith in the banks. This fall in the active money supply is potentially deflationary and would justify the actions of the Bank of England in extending Quantitative Easing.
So how significant is £6 billion of cash hoarding? There are £54 billion of notes and coin in circulation in the UK according to the February 2012 Bank of England Balance Sheet.
While this seems a lot M4, the widest measure of the money supply, is well over £1500bn and most transactions take place electronically. Also the velocity of circulation, how often money changes hands, could adjust to a shortage of cash and further the Bank of England would simply supply more cash in a shortage. However we have a modern example of a leakage from the circular flow due to savings behaviour and that has not happened for a while.
