Romans 12 has a lot going on in it, and unfortunately, being paired with Peter's Confession in Matthew 16 in the lectionary means that it often gets overlooked as a preaching text. Here are some important things to note though, after you've read the passage again.
Living sacrifice - Everyone knows that a sacrifice is dead. To make a sacrifice, you kill an animal or person (looking at you, Abraham), but here Paul let's it be known that God wants the sacrifice of our lives, not our deaths, that we serve God by living. This is an echo of Hosea 6.6: For I desire steadfast love and not sacrifice, the knowledge of God rather than burnt-offerings.
Members one of another - It is bizarre to think about, but Paul wishes us to believe that we are Jesus' body in the world, AND that we carry parts of each other around with us, that we are members of each other. Your Christian brothers and sisters are part of your body. This is the radical unity and reconciliation to which we are called. Kasich-Hickenlooper may be great for politics, but such reconciliation is fundamental for those who follow after Jesus Christ.
The compassionate in cheerfulness - If I were going to pick a virtue to go along with compassion, it would not be cheerfulness. Empathy or caring or concern or strength even. But the more I sit with it, the more I think that Paul is correct, that those who share compassion as part of their Christian life need cheerfulness to keep doing it. A few weeks ago, I was dropping off some cash for a neighbor in need at the Hanover library and then heading to do some hospital visits. I was tired and low on compassion. A girl walked into the library, maybe 3 or 4, and walked up to me and gave me a hug. I didn't know I needed that hug until I got it. But the cheerfulness given to me in that hug carried me through the rest of that day. Cheerfulness is indeed the virtue that goes with compassion.