The Bible does encourage Christians to participate in government for a variety of reasons including being a buffer against  the wrong interpretation of scripture.  For example ,in Daniel 4:27, Daniel told the king to break off his sins; he told him the truth and that way God used Daniel to be  a counselor.  Another example in Jeremiah 29: 7, God asked His people to seek the welfare of the city of there captivity, and to pray for the city.  There is a lot of other examples in the old testament and some in the new testament (Mt 14: 3,4, Luke 3: 18-20) are some examples that God used His people to make an influence for God's larger plan.