To be fair, Americans aren't actually hiding their money in mattresses. Well, at least most aren't. What they are doing is paying down debt at record rates:
U.S. consumers shed some of their debt for the fourth month in a row in May, the Federal Reserve reported Thursday. Total seasonally adjusted consumer debt fell $9.15 billion, or a 4.5% annualized rate, in May to $2.42 trillion. Economists expected a decline. The series is very volatile. April consumer credit was revised sharply lower to a decline of $14.86 billion compared with the initial estimate of a gain of $1 billion. The decline in May was led by revolving credit-card debt, which fell $7.32 billion or 10.5%. This is the 20th straight monthly decline in credit card balances. Non-revolving debt such as auto loans, personal loans and student loans, fell $1.82 billion or 1.4%. Since the collapse of Lehman Brothers in September 2008, consumer credit has declined in 18 out of 20 months.
This decline in consumer and business credit/spending has dwarfed increases in government debt/spending designed to help offset it, resulting in higher unemployment and deflation.
Deflation is nothing more than a decline in the total amount of money and credit in an economy. Less money/credit chasing the same amount of goods results in lower prices. Most believe that inflation can't happen here because the Fed can simply "print money". What they fail to grasp is how exactly the Fed goes about getting that money into the economy--that is, by so-called "quantitative easing", a fancy phrase for using the Fed's newly invented/printed money to buy US government bonds. Notice that, after the Fed buys these bonds, the total amount of money and credit in the economy hasn't actually changed! The Fed simply changed one thing (credit) into the other (money). If nothing else happens, the effect is neutral on prices since prices are determined by the total amount of money and credit available to buy goods.
Now, unlike credit, money can be lent multiple times over. Thus, assuming that the newly printed finds its way into banks and is ultimately lent out, the Fed can increase the total supply of money and credit in an economy, and therefore create inflation, by "printing" money. But, this is a huge assumption, and one that history shows doesn't automatically follow.
In fact, history is replete with examples of times when changes in social mood and/or demographic factors conspired to thwart this assumption--that is, times when people preferred to not to take on more debt but rather to use free cash flow to retire debt or build savings. During such times, the Fed's newly printed money isn't lent out, at least not to the productive (i.e., "risky") segments of the economy (i.e., businesses and consumers).
When do such times occur? Well, they are not common, fortunately. But, they are known to occur when:
(a) the population has aged considerably and is therefore inherently more risk/debt adverse; or
(b) debt (measured as a percentage of total economic output or GDP) reaches unsustainable levels; or
(c) the collective social mood (which runs in somewhat predictable cycles called "Elliott waves" turns significantly negative.
Japan experienced a couple of these conditions over the last 15 years. The result was the "Lost Decade", which is quickly turning into a lost 20 years. However, Japan's deflationary experience was buffered by the fact that the rest of the developed world was still booming at the time. Exports sustained Japan in a way that they can't/won't the rest of the developed world.
The developed world is now as aged as Japan was in the early 1990's. Despite the debt pay down of the last 18 months, developed world debt measured as a percentage of GDP is still near historically unprecedented levels (and nearly twice as high as before the Great Depression), and no one can doubt that social mood has turned decidedly negative since 2000 (a good measure of this the number of terrorist attacks over a period of time and, in the United States, the rise of "third parties" such as the Tea Party). In short, almost the entirety of developed world now faces all three deflationary forces all at once, and at historically unprecedented levels. The result will be a Great Deflation that will remake the world over the next decade.