The trump card here is Article I of the Constitution, which vests all legislative power in Congress. This proposal is nothing more than a direct assualt on the legislative power.
Nearly every committee of Congress – save for appropriations, budget, and rules – is entirely dedicated to authorizing and conducting oversight over government programs. With the exception of pork projects, in a very narrow manner of speaking, the vast majority of government programs are only authorized for a limited period of time. The highway trust fund has to be reauthorized every five years. The Defense Department has to the reauthorized at least every two years, in practice, its reauthorized every year. State Department programs were reauthorized last in 1994 or so, but since then, they’ve basically been reauthorized through appropriations bills.
What the White House is proposing – you can flip through Analytical Perspectives more if you want more details – turns the Constitution on its head. It strips this oversight and authorizing power of Congress and turns it over to a commission that’s part and parcel of the Executive Branch. (You might note that Clay Johnson seemed particularly enthusiastic about this point in the linked article.)
Yes, as you state, Congress would have the power to “veto” the elimination of programs that the commission doesn’t like, but ask yourself a question: Which branch of government does the Constitution give a veto? The Executive or Legislative Branch?
You can’t seriously say with a straight face that the Founding Fathers ever intended the Executive Branch to do what it wants, unless the Congress votes to stop the President. This cockamamie idea turns the Constitution on its head, and reverses the roles of the Congress and the President. I can’t see how anyone can seriously argue that the Founding Fathers would want the checks and balances of our three branches of government to be upset in such a silly way.