Can Christians have compassion?

It has sometimes been pointed out that the desire of many on the left to blame high crime rates and other bad behaviour by poor people on the environment in which they grow up is rather at odds with a liberal conception of people as free and rational agents. It occurred to me today that this is an even greater problem for those who take the bible to be the word of God:

For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse. (Romans 1:20)

The Christian believes that, with two exceptions (and one of them was also a deity) every person who has ever lived has sinned, and grievously so. Despite this ridiculously strong evidence that living without sinning is basically impossible given the human condition, people are still taken to be morally responsible for having sinned.

I can see two ways in which a Christian might push back against this, but both seem to have very severe problems. The first is to argue that going to hell for one's sin does not necessarily imply a moral judgement against one for having sinned; merely, that one is not absolutely pure and therefore cannot be with God who is himself absolutely pure. This is perhaps the easier bullet to bite, but it still means that Divine Command theories of morality are rendered incoherent. This is a serious problem, not only because many Christians would like to identify morality with God's law but also because one of the most popular arguments for God's existence is that it gives us a grounding for objective morality.

The other counter-argument would be that while we cannot realistically go without sinning, we can generally sin less than we actually do. But this makes it difficult to resist the argument that especially virtuous people. who sin but do so at rates for lower than other humans, ought to be (in a sense) justified by their own efforts. "Yes, it's true that I sinned, but it would have been nigh-impossible for me to have sinned less considering that I am, ultimately, only human." This flat-out contradicts crucial Christian doctrine:

Jesus answered, “I am the way and the truth and the life. No one comes to the Father except through me." (John 14:6)