For example, orders to the military would be directly authorized by the Constitution as Commander-in-Chief.
Designating National Parks? I don’t know, but the public has acquiesced over the course of many decades, so probably a done deal unless there is a very brave Supreme Court in the near future.
However, I do think that the President can only implement policies established by Congress through its laws, and the President may not legislate. There is a large gray area between legislation and establishing by regulations. However, most regulations for various agencies and departments are authorized by enabling legislation, and the agency cannot act outside of the parameters of the enabling legislation.
However, there are no rules of there is no court willing to canalize the authority of the agencies of government by a strict reading of the enabling legislation. Therefore, since this is the case, I believe that the President will get by with anything he wants if he goes this route.
Court challenges will be rare, unsuccessful, and predetermined.
Congress has the power of the purse, but this will not stop anything unless they take up the practice of voting on separate bills, so that unrelated appropriations are not combined into one take it or leave it package. It is enforced extortion, but it is the fact of life in Washington.
The Tea partiers will succumb to this process and lament its unfairness while gnashing their teeth at the injustice of it all.
After all, nothing will change.
I would assume they must be authorized by the Constitution or at the least delegated to the executive branch by the Congress, assuming the Congress has the power to so delegate authority in a particular situation.