“The difficulty of getting things done with larger legislative bodies” is not obvious to me at all. Mostly, the structure and traditions of the legislative body in question seem much more important.
In European parliaments for example, party discipline is often very strong, the legislative work is prepared by the parties, the committees and the government. Coalitions in parliamentary democracies iron out a legislative agenda when forming a government at the beginning of the session, sometimes in writing, and mostly stick with it. One exception would be France and its peculiar semi-presidential regime but in this case the president mostly gets what he wants and he is more constrained by business interests, EU rules or potential strikes than he is by his parliament.
Individual members of parliament can push amendments and in some limited cases a small party (or a small group within one party) can threaten to vote against their block on an issue that's very important to them but there is none of the “getting the votes” one-by-one that seems to be going on in the US. Proposals introduced by an MP (as opposed to the government) rarely succeed. Most MPs live and die with their party.
For better or for worse, there are many things that seem to hinder changes or reforms but the parliament usually isn't the most important. And a lot of laws do get passed, albeit not always of great quality (I mean this in the technical sense of “laws that are difficult to implement or have poorly thought-out side effects”, and not merely in the sense of “policy with which I happen to disagree”).
To take but one example, if you look at immigration, you will find lots of pandering, hypocrisy and outrage, not much effectiveness in reaching non-trivial goals, but also an inordinate amount of new legislation. There are countries where governments are engaged in a tit-for-tat game of reversing the previous government's changes or pass a new law every other year to further tighten the rules they put in place themselves. But the size of the parliaments never prevented new laws and I don't know any European country with a US-style stand-off, fueled by individual MP's concern about their personal voting record and ostensibly waiting for some sort of mythical grand bargain.
If anything, it's the fragmentation of the party system or razor-thin majorities that might play a similar role in most parliamentary democracies. A government that is trying to hold together a fragile coalition often needs to be careful not to anger any important group. But individual members and their numbers do not count so much. You see a lot more drama, back-room deals and blockades in the 150-strong Belgian chamber than among the 600 members of the French Assemblée nationale or the German Bundestag.
Incidentally, there are two Swiss cantons that still have a form of direct democracy called a “Landsgemeinde”. All laws must be voted by the whole electorate (well, at least by those that feel concerned enough to show up but that's still several thousand people), assembled once a year on a public square. That's a very large legislative body indeed. It seems to work OK but, as far as I know, instead of degenerating into some sort of free-for-all chaos where nobody ever agrees on anything, it just increases the role of the government even more as even if anybody can ask questions or make proposals, it's mostly those that have been prepared by officials that end up being adopted.