It is pretty common to hear nonchristians say they lack faith in a wistful way, and add that they (sometimes) wish they had it. See Joss Whedon for example.
In the first place, I think this is actually a misuse of language. What they really mean is that they are not intellectually convinced that God exists. Along with this, they often speak on the assumption that “faith” is some kind of mystical intuition that they are lacking.
Faith is not a mystical or any other kind of intuition, other than, I suppose, the feeling some people get that indicates (rightly or wrongly) that they can trust someone else. But even that feeling is based on data, whether rationally or irrationally inferred. I’ve explained here why I don’t think Hebrews 11.6 assumes or implies that one comes to acknowledge the fact that God exists “by faith.”
As I see it, the Bible presents the entire creation as a signal from God, and the only reason we don’t respond properly to the signal is that God (or the idea of God) makes us so anxious that we’d rather pretend the signal is just noise. (Incidentally, Romans 1.18ff has almost nothing to do with this.). Of course, hidden motives are never easy to prove. Self-deception is real, but one side of it entails that the person who claims he is not intellectually convinced that God exists, really is not intellectually convinced. He needs to be argued with, not given orders to repent.
So acknowledging God’s existence isn’t precisely faith. It is more like an immediate deliverance of reason. It is simply an evident truth, like the belief that your friends have minds (one each, I mean) or that the kitchen still exists when you are in the living room.
Faith, on the other hand, is simply another word for personally trusting that God. Trusting him for what? The content of that faith will depend on what specific promises one believes God has made, but in general, by definition, you are trusting God to be faithful.
While I’m not condemning phrases like, “I have faith” or “he just doesn’t have faith,” I do want to be careful we don’t see this as simply some kind of passive absence. We are taught (correctly) that faith is a gift of God, and see it almost as a mystical form of enlightenment. But that’s not it.
Hebrew 11 describes Sarah’s faith this way:
By faith Sarah herself received power to conceive, even when she was past the age, since she considered him faithful who had promised. (Hebrews 11:11, ESV)
This corresponds to the writer of Hebrews earlier exhortation–the reason he gave why his readers should continue in the faith:
Let us hold fast the confession of our hope without wavering, for he who promised is faithful. (Hebrews 10:23, ESV)
The point is that, if you distrust God, you are saying he is untrustworthy. There is nothing passive or neutral about a lack of faith. You are making a positive attack on God’s character.