I've been meaning to watch this clip for a while. I didn't get to see the original airing of the episode of ER, but had heard about the next day during my CPE time. It's a very powerful presentation of actual needs that people have during their pain.
Speaking out of my own chaplaincy experience, I haven't been in such a situation as the above. It's hard, though, to know when to stop asking clarifying questions, leaving people to deal with their own theology and when to come forth with Gospel-centered, Jesus-saturated truth. Knowing when those moments are is difficult and if you miss them, in the words of Donnie Brasco-- Fugget about it.
I was pushed to that point last Tuesday when I went to visit a single mother who was about to lose her baby at 17 weeks, who, again, was conceived out of wedlock. Her poignant question came about an hour into the conversation. We were talking about whether the loss of this baby was punishment for having sex outside of marriage-- which she rightly understood as sin. She asked, "But isn't there punishment for sin?" "Yes, yes there is. But for those who are in Christ, that punishment has been paid by Jesus on the cross." It wasn't the time to ask what she thought; it was time to offer her hope in the midst of her pain and loss. It was time to offer her the Gospel.
Just before I saw the above clip I saw the below one. In it John Piper offers a much different picture of the Gospel of Jesus Christ.