The difference between what the economy is currently producing and what it could produce with full employment is called the output gap. We currently have a large output gap, so the economy can absorb a lot of additional spending. And, in fact, we want a lot of additional spending (higher aggregate demand).
Where your argument is lacking, is that it takes a simplsitic domestic approach, in a global world of resource scarcity. It takes an elemental view of the income function, where it is stipulated that a rise in government spending should equal an equal rise in aggregate output and demand. This is not so in reality. Growth in the economy has and always will be driven by the pace of investment by the private sector, and as indicated by the record low velocity of money, that private sector is happy to invest in financial assets supported by central governments of the world... and not on Jhon Doe opening up his measly business.
Moreover, our level of debt supported by the Fed, has a direct reflection in the relative value of each dollar out there. While you focus on demand-push inflation (people making more money and bidding up prices), the reality is that the US is a net importer of goods, and it pays for those goods with weaker and weaker dollars (price of imports like energy, cars, electronics increase... hence inflation).
The US also depends on foreign borrowing and inflow of cash to cover its current account deficits, but foreign governments and global companies are happy to plug this hole in our balance of payments because the US dollar is (for now) the global reserve currency. They need more dollars to flow out of the US (CA deficit) in order to go about their business using dollars for trade.
If the US dollar loses its reserve currency status, get ready for its relative value to plunge, and for inflation to happen via higher import prices. Before you bring up our exports becoming more attractive, we do not have the manufacturing base anymore to rely on this, and if you need a real-world example, Japan has debased their currency on purpose by +10-15% (don't remember exactly) and they are now running a large trade deficit (compared to a surplus in previous decades).
If you want to be more specific about the current state of the world, the trillions of dollars printed since 2008 have solely gone to financial assets, private funds buying up houses, and to the +$60 trillion dollar finance economy (the shadow banking system), where the 1% leverage up their money to make money from money. It's a nice enterprise for them. Trouble is, if something goes wrong there, us poor folk in the real economy bare the brunt, get our assets seized (ala Cyprus), get our jobs destroyed, and will be paying more taxes when it becomes politically feasible.
Your notions on inflation not happening do not incorporate the fading perception of the dollar as the reserve currency. China, India, Russia, Brazil, the IMF, Europe, ministers from South America... heck even some Canadian dude, are now making the case that the US reign as the world reserve currency is near its end. Once that happens, the inevitable collapse of the fiat illusion will end... just as it has since the origin of fiat currency in 10th century China.