There is a finite amount of real-value in the country at any given time, that is the sum total of all goods, services and IP. In an ordinary economy, this figure divided by the sum-total of all currency issued establishes the worth of the currency. The US is slightly different in that, at the moment, the US economy is not limited to the borders of the US, but also encompasses portions of every economy that uses the petro-dollar as a means of exchange. This makes the numerator of the equation an impossible figure to determine, which can make things seem infinite, but ultimately there is still a limit.
If the Fed had infinite wealth, in the sense of being able to create value rather than merely print money, then there would be no inflation.