Brad Sherman actually said...

We don't need to pass a new AUMF to show the world we support our troops.

Since then, every President has said that they don't recognize the binding power of the AUMF but they will often act consistent with it.

It vests in Congress not only the power to declare war but control over the money that funds military operations.

The fact is that at least in that circumstance the President, and others have as well, simply violated the War Powers Act.