I think there's a lot going on there, but it's interesting...  The Denarius had the inscription, “Caesar Augustus Tiberius, son of the Divine Augustus.”  Jesus was the son of God, not Tiberius.  Augustus wasn't God, and the Jews weren't to have images of any foreign god, which a Denarius was.  

I don't think the Jews were prepared for the answer, they were expecting Jesus to endorse paying taxes or stand against it.  Instead, He called into question whether or not they should even have them in their possession.   One way to look at it...  It sure shut them up quick.