It is your duty to at least state how much work you already have and let the boss decide what to do.

I had a boss who acknowledged it and told me that it's fine if i'm not too accurate for couple of things.

Not saying anything, burning out and just delivering shit work non-stop isn't going to help either you or the employee, your job is to do your best and your boss has to figure out the rest.

Although i have to say i quit that job, because doing half-assed work is nothing which fulfills me.