Our Founding Fathers were not worried about unconstitutional treaties because the ultimate guardians of the Constitution, the States, were the ones required to ratify a treaty through the United States Senate
The second clause of Article VI. of the United States Constitution reads: This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land.