It becomes more difficult, I agree. I am influenced by my father, an atheist, who was the most moral man I suspect I will ever know. He just was. His values, his honesty, his courage (the ups and downs of his life are almost worth a novel), by example, guide his three sons as we continue on this mortal coil, until we depart. I hold my two brothers in very high esteem, because they have earned it, even though they unlike me, are generally political liberals.
Yes, it's possible to be morally upright without being religious. Partly, it's because non-religious people have the religious heritage there in society to draw on, even though they don't accept its basis. Partly because, as St. Paul says, "the law of God is written in the heart"-- What's known as Natural Law.
I just did a Google search for that phrase and turned up a couple of good articles and books on the subject by writers I know, particularly J. Budzewzski and Phillip Johnson:
http://www.google.com/search?sourceid=navclient&ie=UTF-8&rls=GGLG,GGLG:2005-46,GGLG:en&q=law+of+God+is+written+in+the+heart
But without the support of religious faith it's a lot harder.