Is inflation a lack of production? If every person in America was given a million dollars what fundamentally changes that causes prices to rise? Intuitively I was thinking that this is simply a production problem. With more money there is more effective demand but without a rise in productivity prices will simply shift to a new equilibrium.

I had this thought and I was wondering if it's a good way to understand inflation.
Yes, this appears to be correct. This intuition is fundamentally Keynesian. 

Consider the AS-AD curve.  During the vertical portion, additional demand increases prices while supply remains roughly fixed. As a result, prices increase dramatically.

https://en.wikipedia.org/wiki/AD%E2%80%93AS_model