Does "can hardly" mean the same thing as "there's no way?"
I can hardly ____________
There's no way I can _______
Do these two mean the same thing? What's the difference, if any?
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"I can hardly" can be used literally to say you can do something but only just.
I can hardly lift this heavy object.
Or it can be used figuratively to mean you can't or won't do something - in the same sense as "There's no way I can ..."
I can hardly be expected to write all this code myself.
They mean essentially the same thing, but there is at least some difference in the level of emphasis contained in each expression. I would say that "can hardly" is not as strong as "there's no way" in the instances you show above.
Edit: I am shamed to admit that I didn't even think of the "barely able to do something" sense of can hardly which @Martin Beckett explains so clearly in his answer -- even though that's the more common meaning.
"I can hardly do something" literally means "I can do this difficult something"; the adjective "hard", here synonymous with "difficult", is transformed into an adverb similar to its antonym "easily", and applied to the verb to imply that although possible, the task is difficult or can just barely be done. In fact, "barely" can be used synonymously with "hardly"; "I can barely do something" has largely the same meaning and connotation. It is often used figuratively as an understatement; "I can hardly believe you did that" can really be taken to mean the speaker didn't believe it possible, but since the speaker has probably witnessed it occurring, it must have been.
By contrast, "there's no way" implies impossibility; there is no series of events that would result in the proposed outcome. Though the meanings are clearly different, the two terms are often used in the same context; to express extreme doubt in the possibility of an action.