It's not clear to me where he is getting his data or even what data he is using. I have previously posted data on the growth of the deficit. The actual growth in "currency" is a little trickier since you have to decide what constitutes currency. For now, the primary measures are M1, representing actual currency plus checking account balances, plus M2, which includes other highly liquid deposits such as savings accounts. When Clinton became President, the value of M1 + M2 totaled about $2.8 trillion. When Bush was inaugurated the second time in January 2005, the total stood at about $5.3 trillion and when Obama became President, the total was about $6.3 trillion. The growth was attributable to a combination of two factors: massive deficits incurred under Bush, and a conscious policy by the Fed to expand the money supply because they felt it was restricting real growth during the first Bush term.
If you want to track this information, it is published every Thursday by the Federal Reserve Bank. The growth slowed dramatically in the second Bush term because of the Fed's efforts to contract the money supply by raising interest rates. I do not see growth curves that in any way reflect the graph described by Beck. However, I only looked at data through February 23, 2009 -- maybe Beck's growth happened last week.