Can the government be compassionate?

An old friend of mine made the case that, as Christians, we should utilize the government to protect and love one another because "the government is the people". I find this to be a dangerous proposition and one that subverts the proper roles of church and state. I responded (slightly edited here) by describing what I understand the roles of Christianity and government to be. I'd be happy to receive any and all constructive comments!

The "government" is not the people. It is an establishment based upon a social contract that "the people" have negotiated with each other to uphold order. Still, even if the government IS the people it is not "the church". We have established the separation of church and state for a reason. People must live according to their consciences. The problem is that a government that dictates morality is not made to allow people to do that. In fact, a government is made to coerce, whether for good or ill. That's the difference between the roles of church and state! The government coerces by threat of force (i.e. pay your taxes or you're going to jail), and the church coaxes with chords of love (i.e. Jesus telling his disciples to follow His example). The government is not a savior but should be a blind arbiter of justice. Therefore it cannot love people. And if you will posit that justice is love, then my response will be that love is sorely lacking if it is all justice and no mercy. The law would fall apart if it was subject to mercy and it is the provenance of the government to uphold law (justice) blindly!