Most of the time if a position isn't working out there's stress on both sides. An open, honest discussion can go a long way here. Sometimes you'll find that while the culture wants to challenge and push you to the extreme (or you feel challenged beyond your ability because of the work and the people around you), talking to your supervisor can sometimes reveal that people think you're doing much better than you are. Many places aren't so great at mentorship and people can come away feeling like they're doing a crap job when in reality they're doing much better than the other new person next to them.
This happened to me once when, after being in a new position for about 5 months, I basically walked into the company's owner's office and was ready to offer up my job. He assured me I was doing much better that perhaps the company let on, but that the company just has extremely high expectations, so there wasn't a lot of praise to go around for good work.
Another thing to remember is that a lot of time and effort goes into training and hiring on both the employee and employer side of things. However, if someone truly isn't working out, it's often a relief to both parties if the employee sees this, brings it to their supervisor, and puts a plan together before waiting for what might become an inevitable quitting or firing. The important thing is not to fear the quitting or firing, but discussing openly what's really going on, and trusting that you can work it out.
I've been in stressful/high speed crazy employment situations a few times. One time I wasn't performing up to expectations and I knew it. I was unhappy and was looking to actually change positions within the company rather than quit. I was also doing this inside a company culture where people didn't sympathize with hardship or challenges so much - it was a "sink or swim" kind of place.
So, I decided to talk honestly to my supervisor, even though I felt (at the time) that I might be risking my job doing so. The conversation went something like this:
My supervisor's name was John:
Me: "Hey John. I'm really struggling out here, and to be honest I'm
not sure I'm very good at being a Team Lead. It seems to me that,
while I could learn to be a pretty decent manager, I've certainly
discovered that I don't have a passion for it, and I think it's
affecting my work."
John: "I agree."
Me: "I also think that I have talents that could be better used
elsewhere in the company. In fact, I'd really like to try to move into
a position in [some other department]."
John: "Well, Jeff. I really appreciate you coming to me. I see you're
not doing so well, and yet in terms of time in the position, you're
one of the most senior Team Leads we have right now. I agree that
you've got definite skills, but here's the thing: I can't move you out
of your position (even if we both thing you'd be better there) without
you really giving me something. What you're asking for is basically a
promotion. I can't move you into a new role until I see you get your
team into shape. Look at your team's performance numbers. This is
garbage, and I think we both know that."
Me: "Yeah, it's not good. What's it going to take to get this fixed?"
John: "I'll tell you what. You get [performance numbers 'x' and 'y']
to [this metric], and we'll talk seriously about this."
What this conversation did for me was a couple of things.
First, it lowered my fear of just talking honestly about a problem by simply pointing out the elephant in the room. John, certainly, was feeling that he was having trouble getting me to meet my performance numbers, and I felt the stress of trying while feeling that my skills were probably better used in a technical role, even though it was my own actions in previous years that got me into a management role in the first place.
Second, it put John into a position to set a really clear goal for me: get 'x' to given metric - that's all I had to do. Since I was unhappy in my role, and by mutual agreement I wasn't living up to expectations, the two of us had a clear place to go, and a simple way to measure my progress.
Given that we both agreed upon the problem, and the goal was clearly stated, it was up to me to get myself out of the problem. My fear was assuaged when I realized that rarely (unless a company is downsizing) does an employer just flat want to get rid of someone. By opening a conversation, you can really help yourself out of things. This simple conversation, however, led me to getting out of that position and into a better one in less than 8 weeks.
I eventually left that company a year or so later, after I realized that the culture fit just wasn't there. However, I left on great terms, knowing exactly what it was I wanted in my next role, and in a good relationship with my former employer with a recommendation to boot. The good parting happened largely because I was honest with myself, and I brought my boss into a place where we could just talk it out.
People can be a lot more reasonable than we fear at times.