In all honesty it doesn't even have to be large, it suffices to be powerful. Like the President. If you're the president, you don't really need the 535 people from congress to act with you. You only need them to not act, which they can be relied on to do more often than not. (In fact, I believe you don't even need all 535 of them to not act, only some of them can take the action of "no action" and you can do what you wish.)
What we have learned is that you only need the Senate Majority Leader to refuse to act. It turns out that is the crucial weakness in the US government with no checks and balances on it. And, of course, isn't in the US Constitution.