In a sermon on Romans 12:1-2 addressing the issue of homosexuality and the marriage amendment, Piper argues that we must approach life on this earth from two perspectives: as indigenous and as pilgrims. As indigenous to the people we are a part of, Christians should get involved in the law-making process. He says,
We should pray and work to shape our culture, its customs and laws, so that it reflects the revealed will of God, even if that reflection is only external and dim and embraced by unbelievers with wrong motives. . . . If someone asks, Why do you impose your religious conviction on the whole culture, we answer: all laws impose convictions on a culture. And all convictions come from worldviews. They don’t come out of nowhere. People argue for laws on the basis of a certain view of the world.
He argues that we should work as indigenous people to make our world better.
He also argues from the perspective of the pilgrim when he says,
On the pilgrim side of the tension, we make our Christ-exalting, cross-centered, soul-saving biblical worldview known with brokenhearted joy. Joy because Christ really is the sovereign Lord of the universe and will establish justice and purity in due time out of this fallen world. And brokenhearted because we share in the pain and misery of what sin has brought on this world. . . . The salt of the earth does not mock rotting meat. Where it can, it saves and seasons. And where it can’t, it weeps.
I don't think this answers the question, but it does help us frame the question a bit more clearly. We must be engaged, but we cannot leave all our hopes and dreams in the hands of government.
We have a greater hope.