Of course, Schumer got it totally wrong. The three branches are legislative (Senate & House), executive (president), and judicial (Supreme Court).
Ed Morrissey brought up some good points about the rest of what Senator Schumer was saying:
But even apart from that, Schumer still doesn’t have a point. No one is saying that we shouldn’t pay the debt ceiling. There isn’t anyone rooting for default in either party. The question before Congress is whether we will raise the debt ceiling in order to allow the government to borrow even more money. If Congress doesn’t raise it, the US won’t be able to sell more debt, which means that it will have to stop paying on its obligations, although those decisions can be prioritized to put off defaulting on existing bonds, at least for a short period of time.
So, Schumer didn't know what he was talking about all the way around.