If two characters in a story, a male and a female, are given an infinite number of tasks to perform, could they go back in time and hook up with duplicates of themselves, then go back in time further, and mate with each other to produce descendants, and then encourage their descendants to also go back in time to clone themselves and mate with duplicates of themselves, who would also go back in time and clone themselves and mate with their previous perspective partners, to create more descendants, etc. etc. etc. -- until they create an infinite number of temporal duplicates, clones, descendants and so on?

Could an entire infinite series of duplicates of duplicates perform an infinite number of tasks?

they can if you say so. And the opposite is also true.

While I'm sure your story could swing it if you say so, if you're going for extreme realism (well, as close as you can get with this interesting scenario) I would say no. Two mulitiplied by two by two by two by two and insane number of times is still a finite number, even if it is too high for humans to count. I'm not sure that time travel can create an infinite number of anything. Infinite loops maybe (kill your own grandpa and you don't exist, so you weren't around to kill him, so he lives and you're around to kill him again, meaning you don't exist to kill him anymore, etc.) but not infinite objects or people. If you'd like to dig into the "infinite alternate dimensions" theory, though, it could be totally plausible to get infinite descendants.

Then again, you could take the above poster's advice and just invoke Willing Supension of Disbelief and say it worked. Most audiences don't read too far into this kind of thing and the vast majority of the ones who do will forgive you if the story is well done.

-Spark