Now onto the practice, I set forth below a long recital of the history of the enactment of international agreements showing that the practice has long preexisted Obama so there is plenty of political cover for the Senators (also including Ted Cruz, to be fair). I need is unconstitutional but I also acknowledge that it is an established practice. In this context, Ted Cruz's vote is not quite so far off the conservative reservation.
Here is the Wikipedia analysis (https://en.wikipedia.org/wiki/Treaty_Clause):
In the United States, the term "treaty" is used in a more restricted legal sense than in international law. U.S. law distinguishes what it calls treaties from congressional-executive agreements and sole-executive agreements.[1] All three classes are considered treaties under international law; they are distinct only from the perspective of internal United States law. Distinctions among the three concern their method of ratification: by two-thirds of the Senate, by normal legislative process, or by the President alone, respectively. The Treaty Clause [2] empowers the President to make or enter into treaties with the "advice and consent" of two-thirds of the Senate. In contrast, normal legislation becomes law after approval by simple majorities in both the Senate and the House of Representatives.
Throughout U.S. history, the President has also made international "agreements" through congressional-executive agreements (CEAs) that are ratified with only a majority from both houses of Congress, or sole-executive agreements made by the President alone.[1] Though the Constitution does not expressly provide for any alternative to the Article II treaty procedure, Article I, Section 10 of the Constitution does distinguish between treaties (which states are forbidden to make) and agreements (which states may make with the consent of Congress).[3] The Supreme Court of the United States has considered congressional-executive and sole-executive agreements to be valid, and they have been common throughout American history. Thomas Jefferson explained that the Article II treaty procedure is not necessary when there is no long-term commitment:
It is desirable, in many instances, to exchange mutual advantages by Legislative Acts rather than by treaty: because the former, though understood to be in consideration of each other, and therefore greatly respected, yet when they become too inconvenient, can be dropped at the will of either party: whereas stipulations by treaty are forever irrevocable but by joint consent....[4]
