Dale Earnhardt, Jr. - Everyone here has already said it, the man just seemed to lack the drive and passion to chase wins and titles. The circumstances in which he raced in, carrying the weight of being the most popular driver and having everyone root for him, as well as the depression of losing his father just seemed to psyche him out.
Denny Hamlin - He stays psyched out. Even when he's at his best these days, it feels like his best is not much compared to other current drivers' bests. 2010 did him in, and I don't imagine he has gotten over it. He'll go down as one of the winningest Cup drivers without a Cup title.
Kasey Kahne - The word I have always heard in association with Kasey Kahne has been "potential". The "potential" he has has not been shown a lot, especially in recent years. Glimpses, maybe, but those few moments are ultimately not enough. It's a shame, I genuinely like the guy, have had the pleasure of meeting him, and really hope his tenure at LFR bears fruit because his career is meeting a dead-end, otherwise.
Kyle Larson - He's not very bad about psyching himself out, but he has his moments. Larson tends to overdrive, as noted here several times. One particular race at Charlotte (last year, I believe) saw him throw away what was a certain victory after smacking the wall as a result of just trying to run up way too high... which has happened several times. That brings a race he endured at Eldora to mind!
Chase Elliott - I figure Chase will break through and swing the monkey off of his back, but as it is right now, he's gotta be one of the most psyched out drivers. There's nothing wrong with self-criticism, but he is the king of self-criticism... he over-analyzes his own mistakes a little too much. Once he wins, I doubt we'll be seeing that side much anymore.
Tony Stewart - Arguably a mentally strong driver, towards the end of his career, he faced some grueling trials and tribulations that really seemed to hurt him physically and mentally, which is why Sonoma 2016 was all that much more sweet.
Matt Kenseth - Martinsville psyches him out. He either wants to run people through the wall, or punch them in their head when he races there. @BobbyFord
Upon much consideration and thorough review, I conclude that Paul Menard is the most psyched out driver of all-time. Having his picture taken is a challenge.