We do each have an absolute limit of what we can do at any given moment, but it is not where we think it is. While I hate the "give 110%" expressions, the idea they are meant to convey is valid. The best example is the 4-minute mile. For many years it was thought to be beyond the physical limits of a human. Then Roger Bannister ran a mile in less than 4 minutes, and suddenly others can, too.
Of course, even the absolute limit can often be moved (that's why I said "at any given moment"). Right now, there's a limit to what I can lift in a bench press. No matter what someone says or what I do, I won't be able to lift more than that absolute limit today. But that limit can be moved. For me, a bit more shoulder rehab will double what I can lift in the full range; after that, exercising near that limit will allow me to push the limit up.
Part of our training in MA should be (IMO, though that won't necessarily hold for everyone) occasionally pushing our limits. Most people, when they start a running regimen, think they are "done" at some point in their first run, but they can usually actually run a good bit further (if they haven't run too fast). Our bodies have built-in survival cues that tell us to stop before we get near our limits in endurance. Pushing past that point appears to be linked to willpower processes, so it's something we can practice and improve. Every time we "push the limit", even a bit, we improve our ability to push that limit.
@drop bear posted something about this in another thread recently, and I suspect it's also part of what makes their 12-week fight prep work in the gym he trains at.
This is why many seminars work students so hard, why many TMA schools have a few days a year when they work especially hard (I've heard them called "sweat days", "Summer breakthrough days" and many others). For those training seriously and putting in many hours, they should make sure they're pushing the limit on a relatively regular basis. Training 20 hours a week without pushing the limit isn't as useful, IMO, as training 10 hours a week and pushing the limit 4 of those hours.