"I don't see how they could manage that without a full-scale invasion and control of Iran" - that's precisely what they're saying, and that the domestic populace wouldn't put up with it.

I suppose "could" here is a bit of a stretch. Like technically, yes, you could if you whipped up your country into enough of a frenzy to support it. Hell, Iraq happened (twice), so I suppose it has historical precedent. And yes, a full-scale invasion of a fully committed US military should absolutely be able to conquer and hold Iran. But I can't imagine any circumstance where that's possibly going to happen in today's reality (outside of an Iranian terrorist event on USA soil, for instance).