But, Senate Republicans have prepared their counter-attack. They wrote a letter to Yellen indicating that the agreement should get treatment, not as a law, but rather as a treaty. As a law, it will need only a majority in each chamber. This is hard enough, as Senate Republicans try to prevent a majority.
If the agreement got dealt with as a treaty, then it needs two-thirds ratification in the Senate. Time and again, agreements have died trying for the Senate two-thirds for ratification. The most famous is the Treaty of Versailles in 1919, ending World War I. Senate Republican isolationists defeated that treaty. They thereby crippled the nascent League of Nations, thereby unwittingly rolling out the carpet in the 1930s for German, Italian and Chinese aggressors.
That Senate obstacle is still there. The U.S. has not ratified any international human rights treaties since December 2002, when it ratified two optional protocols to the Convention on the Rights of the Child.