Obama and negotiators attempted to walk the line between agreement and treaty by making some of the deal’s aspects legally binding but others not. For instance, Obama called transparency of climate data and reporting requirements legally binding, but not the goals for emissions reductions.
But “politically binding” isn’t that binding if you’ve garnered no political buy-in. The American system offers several ways to do so with international agreements, and the supermajority threshold of a treaty agreement assures broad political backing. Another way would be to run on a promise to sign a giant, international climate agreement that would commit the United States for decades to significantly reduced emissions and payments to other countries. Obama did neither.
Trump, on the other hand, ran on a promise to withdraw from the deal. To the extent the deal was “politically binding” on Obama, it’s close to the opposite for Trump. Trump’s daughter Ivanka, her husband Jared Kushner, and Secretary of State Rex Tillerson have reportedly been urging him to remain in the agreement since he assumed office, backed by a chorus of energy-industry lobbyists who support the deal.