"President and 2/3 of the Senate in the form of a Treaty."
JN, Actually, the wording is "provided two thirds of the Senators present" {Article II; section 2; paragraph two; sentence one}. Treaties can {and have} been ratified by MANY Senators less than Quorum present. As few as three would suffice. Peace and love, George.
Source for this? The Constitution is unambiguous in requiring a majority of each house present in order for that house to conduct any business.
Not constitutionally.
Section 5. Each House shall be the judge of the elections, returns and qualifications of its own members, and a majority of each shall constitute a quorum to do business; but a smaller number may adjourn from day to day, and may be authorized to compel the attendance of absent members, in such manner, and under such penalties as each House may provide.