Question for Christian conservatives

[The Mikado]

Considering that the Judean and Galilean peasant had to pay not only a hefty tax to Rome, but a significant Temple Tax to the priestly elite in Jerusalem (rendering unto God what is God's), the quote is actually kind of brutal. 

Like most of the stories of Jesus and the Pharisees, it's them trying to force him to answer a provocative question with either a treasonous answer (don't pay taxes) or an unpopular one (pay taxes), which Jesus gets out of with clever wordplay and skilled misdirection to avoid answering the question.

[The Mikado]

Those symbols speak of liberty and republicanism, which is the opposite of the imperialism of Caesar.  Our currency bears images of George Washington and Thomas Jefferson (they would not have approved of being there) who fought against the idea that all wealth belongs to the king. 
If you want to use this passage to justify the government owning all money, you also have to accept as normative the authoritarianism behind Caesar's imperial economy.

Carry a lot of two dollar bills?

To Frodo: taking the concept at face value (all coins with Tiberius Caesar's face on them belong to the state) is a rather absurd proposition, as it would rule out any sort of economy whatsoever.