1. That consent from the Senate can be inferred.
2. That since treaties are laws, according to the Supremacy clause, they must be treated as laws, and therefore, the House and Senate must agree to withdraw, and the President must sign off on it.
I find option 2 more compelling, because it is based on specified language in the Constitution. Treaties are laws. Surely, we are not saying the President can undo a law on his own whim? One could argue that since the House is not involved in ratification, they should not be involved in withdrawal. I can appreciate that. I am not 100% sure. But I am sure that what the President is doing--and the GOP is supporting--is unconstitional. Conversely, Jerry Nadler was upholding the Constitution today. It just shows how low the fat socialist bastard is willing to go.