As more than 190 nations continue to meet this week to negotiate an agreement to limit greenhouse gases, President Barack Obama finds himself in a terrible bind.

On one side is international pressure to vest any climate deal with what international law considers to be binding legal force. On the other is the political difficulty, even the impossibility, of approving a climate treaty under our Constitution because of the need for approval by two-thirds of the Senate.

To realize the purported benefits of limiting greenhouse gases, nations must undergo the economic pain of reducing carbon-based fuels. Because all nations benefit from any reduction, individual countries have an incentive to keep polluting and just free-ride on others’ efforts.

In November, French President Francois Hollande declared that if a Paris agreement “is not legally binding, there is no agreement.” (Of course, in international law, there is no way to compel compliance, judicially or otherwise, which is what makes such law an amorphous concept.)

The Obama administration has made contradictory statements about whether a Paris agreement will be binding. Last month, Secretary of State John F. Kerry said that any deal was “definitively not going to be a treaty.” State Department officials backtracked the next day: “The U.S. is pressing for an agreement that contains both legally binding and non-legally binding provisions.” In the summer, officials said they would negotiate a “politically binding deal.”

Obama may try to thread the needle with an executive agreement, which does not involve Senate consent. The U.S. has made roughly 1,100 treaties in its history, but it has made about 18,500 executive agreements — 17,300 of them since 1939. While attractive to all presidents, executive agreements rest uneasily under the Constitution, which authorizes treaties only.

Obama’s recent Iran nuclear deal illustrates the line between treaties and executive agreements. While we opposed the nuclear deal’s substance, we conceded its form as an executive agreement. The Iran deal did not limit American sovereignty, it did not take attacks off the table and it required no new legislation.

In our view, it fell within the president’s power and will probably last only as long as his time in office. (A president has the unilateral power to abrogate executive agreements, and even treaties, as George W. Bush did in 2002 by withdrawing from the Antiballistic Missile Treaty).

When it comes to a climate deal in Paris, an executive agreement cannot meet the “legally binding” demands of European leaders because the president alone cannot keep the promises that are under discussion. For example, the Paris negotiators want firm emissions-control agreements.

But only Congress can set specific national limits on greenhouse gas emissions under its authority to regulate interstate commerce. Helping developing nations absorb the costs of energy limits, as envisioned by a proposed $10 billion Green Climate Fund, would also require legislative approval: Congress alone controls the power of the purse and any U.S. contributions to the fund.

Obama can achieve his climate change legacy only through delicate negotiations with Congress. His poor relations with the House and Senate, especially on foreign policy, appear to render success unlikely. Obama may rely on his unilateral authority to join a world climate pact, but without Congress his most important promises will be empty ones whose fate will be left to his successor.