You’re probably going to have to use some Javascript to control this — WordPress can’t (although there might be a plugin available, haven’t checked).
You’d have to start with setting the maximum number of words for an excerpt (say, 500). Then the Javascript would detect the screen resolution (probably upon load and screen resize), and then based on that, take off the appropriate number of words from that original 500.
That’s the trickiest part I think, cause you’d have to convert the original 500-word excerpt into an array of words, and then take a number of elements in the array to write it out again word for word, until you reach the number of words you want.
I wouldn’t be able to explain the full details but I would say that’s the theory behind it.