Q, You need to remember that there is a difference between treaties and "ordinary run of the mill" laws. The problem is that DG, and others want to reverse the duties of the presidency and Congress in the making of LAWS, not treaties. It is an effort to parlaimentarianize the U.S. of A. form of representative constitutional government. If they were making these "agreements" as "treaties", there would be no constitutional question. But they are NOT! We should maybe ask, "WHY NOT??" Peace and love, George.
Basically, look at this, especially the part that reads:
"...1928 case in which the Court, speaking through Chief Justice Taft, upheld congressional delegation to the President of the authority to set tariff rates that would equalize production costs in the United States and competing countries."Setting tariff rates is specifically granted to Congress in the Constitution ("Duties, Imposts and Excises"), yet it is allowed to be delegated to the President.
The clause granting the power of tariff to Congress is only a couple above the commerce clause. The other two items in the commerce clause besides foreign governments (states and indians) have been delegated already to some extent in the form of the Interstate Commerce Commission (now Department of Transportation) and the Bureau of Indian Affairs.