I had come to the conclusion a while back that congress cannot by statute limit the power of the executive as granted by the Constitution. It takes an amendment to do this.
I have seen some good arguments to the reverse like this one about default vs inherent powers, but in the end they failed to convince specifically because of THIS line of argument:
If it is true that congress can by statute limit the constutionally granted powers of another branch, then why can't congress require a supermajority, for instance of the Supreme Court (like 6-3 or 7-2) in order to reverse decisions already taken (like Roe vs Wade or more to the point, like Plessy vs Ferguson). After all, a simple majority is nothing more than a default setting.
However now via Powerline comes more on this.