It varies from place to place, of course, but speaking as a software developer, there is strong reason to NOT want to ascend to higher tiers within a company, usually because it involves
doing less of that technical thing you like/are good at and more doing other stuff like managing people and projects.
Some companies will accept a "thanks but no thanks" to a promotion offer; I've literally told my boss, "no, I'd rather keep doing more or less what I'm already doing but for more money" and he was cool with that. Some companies have specific titles to give out so that HR is happy with you getting promoted while really just having the same job but for more pay; in software it's usually Junior Developer -> Senior Developer -> Staff Developer or Senior Systems Architect or what-have-you. Other companies, not so much. You'll need to judge for yourself how well a "thanks but no thanks" response will be taken.
So yeah, kick this task's ass and, if it isn't suicide, feel free to remain where you are if that is what's working out for you.
EDIT: A grizzled old QA guy I used to work with would say, "The reward for doing an impossible task is another impossible task." There's nothing wrong with working on harder stuff sometimes, or having to deal with an emergency that sucks profoundly. However, if your responsibilities really are expanding and you're being pushed into a new, shittier position one inch at a time, stand up for yourself... again, assuming your company doesn't demand seppuku from that sort of behavior. Some companies just plain suck and a reasonable job will become an unreasonable one without affording you any recourse but to quit. But others will respond to an underling piping up and expressing justified concerns.