Whenever I've accurately felt this way - not simply feeling overawed by the height of mountain to be climbed - it has typically indicated: 1) lack of empowerment of IT teams to push back on features and deadlines; 2) poor grasp by business stakeholders of availability and ease of reallocation of IT assets; 3) unrealistic goals by project owners or managers.
I no longer accept impossible terms. If I identify factors that create a seeming "impossibility state," I offer the managers and owners options to restore a state of non-impossibility, e.g., more time, more money, fewer features. Replacing me, the troublesome doomsayer, is an option...prob'ly won't fix the impossibility issue, but, hey, no more of that bothersomely distracting, truthy stuff. If I present an impossibility finding and it's rejected without CONVINCING counter-argument, I won't continue without an explicit waiver of liability.
I've been programming, analyzing, architecting, and engineering software and data solutions for over three decades. I'm a mathematician with formal education and professional experience in the methods of Advanced Statistics, Operations Research, Decision Theory, and Project Planning. I don't casually say "impossible" - if I say it, I can back up my claim with non-trivial arguments.
I can help tame the impossible in shops that aren't crazy, and I won't work for a crazy shop more than once. However, I only seek part-time and temporary positions these days, and hence, I'm less locked-in than most captive employees or even small business owners (my bride's a working professional - I eat and sleep indoors, whether I work or not).
TL;DR: Yes, I've labored on "Impossible" projects - will NOT do it again. Hard? Fine. Impossible? Nope.
I tend to work on systems where it's never "done". Always a new feature to add, tweak to existing functionality, this customization, that customization, this regulation to meet, that report to create, and so on and so on and so on.
I've felt that way pretty much every time I've started a new project.
When we started building hipchat server, it looked like it was impossible to be able to ship a SaaS to enterprise customers as a VM, yet we ended building and shipping it.
Now that I started my own company, I've been through a lot of those moments. Whether is when you start thinking about it, getting those first customers or fundraising, there's a point where every non-trivial task feels impossible. And then the day you do it, you realize that it wasn't that hard, you celeberate, and then move along to the next "impossible" task.
dhanushka madushan
Software Engineer @WSO2
This happens every time when I join with a new task. In the beginning, it is stressful to work and feel it is impossible to complete the task. But when the work is going on I feel I am reaching the goal. Once the tasks getting completed, that happy feeling cannot be bought for money.