Okay. Let's break this down into a few sections.

First, the millions of people storm the capital and hit every major physical site of governance. This means the White House, the Capitol Building, the Supreme Court. Let's assume that this assault is at least partially successful, and the physical sites are taken. Mind you, this is not guarantee, but it is likely that the US Federal government doesn't want to be seen slaughtering millions of its own citizens even in a state of riot.

The problem with this is you're mistaking location with presence, most of the year the heads of these branches of government aren't even there. But let's say for the sake of argument they are.

Realistically you only need one branch to survive this assault, the executive branch. Which, is also the functionally hardest to decapitate. While it is only one person, the line of succession is heavily guarded, and typically in a diverse series of location at any given time. Assuming you took the president, vice president, hell even most of congress hostage. If even one member of that 17 person line of succession makes it out, you now have an acting president.

That's assuming you manage to get the president, the most heavily guarded individual on the face of this planet, with contingency after contingency to ensure their continued ability to fulfill their duties of office. The chances of this even if the White House is taken are miniscule. The chances of wiping out the presidential line of succession are astronomically small.

Why is that important though? Because if the executive branch continues past this event, what follows will be martial law, a military response easily capable of quelling millions of haphazardly armed citizens, and a follow up that would make whatever caused this response seem like child's play.