At what point does the growth of the population demand (require/suggest/whatever) that the House expand? What logistical challenges exist? I see that politically, there would be little chance of anything but a doubling to 870, but that would require a massive increase in office space in an already crowded area of DC. Still, the number of constituents per Representative has to peak at some number, right?Ah, an old Plain Blog favorite. My position on this is that a Big House (of Representatives) is an intriguing idea, but ultimately a bad one.
Basically, once you have over 100,000 constituents in your district, I'm not sure how much it matters for representation whether it's 500K or 500M. Well, at least whether it's 500K or 5 million. Either way, you're not going to be personally interacting with very many of them.
What a big House would do to the governing of the House, however, isn't any good. It would mainly produce more backbenchers -- folks who would have no real responsibilities (or opportunities) for legislating beyond just showing up to vote. That's already a problem with the House, and it's one that increasing the size would almost certainly make worse.
American democracy works best when individual Members of Congress do serious legislating; that's the whole point, the whole advantage, of having separated institutions sharing powers. Much better to have a huge district with a Member who actively tries to represent the district and has some capacity for action than a much smaller district with a Member who can do little more than vote with the party on the floor or in committee.