What "smaller countries" vote on everything? Or in other words, what countries other than just Switzerland practice direct democracy regularly and systematically at the national level? I think there are none. The USA with its state-level ballot measures / ballot questions is probably the closest thing so far - at least until the EU possibly gets an practicable implementation of initiatives and referendums.
Anyways now to correct the other bit: The notion of direct democracy in Switzerland means that people can collect a percentage of the population's signatures -it is specified in absolute numbers, but saying it like this makes the point more obvious- to "forcibly" initiate a public vote on new laws, or (more easily) stop new laws passed by the government.
As you might guess, the "collect signatures" part very much limits the number of issues that actually will be voted on, and they only get voted on on the national level if it in fact is a nation-wide law that needs to be passed or undone- so no hindrance in practicing the same in the USA, really. They often are simply taken on consequential issues parliament has either not wanted to decide yet, or that parliament has decided wrongly or insufficiently. An example of what one issue that probably would not have dragged on for so long with the right to initiate a vote in the USA: Recompensating any 9/11 first responders for illnesses they may have contracted.
Apart from all that, specific kinds of laws, like changes in the constitution or specific areas of the law may also just simply require a public vote. Even parliament itself can initiate a public vote so they don't have to decide an issue... but you already know that from your own legal practice, except it never happens on the national level, as far as I can tell.