Is there any limit to the power of the President to make treaties?

The power of making treaties is so great that the Constitution will entrust it to no one man. Even the President cannot make a treaty without the consent of the Senate of the United States; nor is it sufficient that a simple majority of the Senate agree to it; two thirds, that is, a super majority of all the Senators who are present when the vote is taken, must agree to any treaty before it is binding on the United States.