President Barack Obama’s latest emissaries to Egypt, Sens. John McCain, R-Ariz. and Lindsay Graham, R-S.C., returned to Washington this week with little to show for their efforts. They tried, and evidently failed, to arrange an end to the nearly two-month standoff between the military government and the recently ousted Muslim Brotherhood. That impasse has brought parts of Cairo to a near standstill.

The senators gave the military leaders a powerful incentive — the potential loss of U.S. aid — to refrain from further violence. Whether this will cause the generals to hold off on their threat to disperse the two Muslim Brotherhood encampments in Cairo by force remains to be seen.

All of the president’s emissaries to the two sides in Egypt’s deepening confrontation, including the two Republican senators, Deputy Secretary of State William Burns and, by phone, Defense Secretary Chuck Hagel, have stressed the need for dialogue. They have asked the military government to free deposed President Mohammed Morsi and other Muslim Brotherhood leaders from jail so that they can participate in the discussions about ending the constitutional crisis.

This has had the effect of alienating supporters of the popular military takeover — the many Egyptians who fairly felt betrayed by Mr. Morsi’s authoritarian actions as president. Indeed, President Morsis appeared increasingly intent on establishing an Islamic dictatorship.

Among President Obama’s messengers, however, Sen. McCain seems to have been the one who stirred up the most anger from the Egyptian military’s backers. When Sen. McCain repeatedly called the military ouster of Morsi a “coup,” he implicitly threatened to force a cutoff of U.S. aid to Egypt, a sum that has averaged $2 billion a year for the past 44 years, including $1.3 billion in military aid.

America’s national interest in Egypt remains clear: It has long served as a source of relative stability in the Middle East. And while Mr. Morsi’s forced exit was necessary, the military must eventually keep its promise to move Egypt toward a self-governing democracy.

But U.S. law requires the suspension of aid to a government that takes office by force. So the White House and State Department have pointedly refrained from calling the Egyptian military ouster of President Morsi a coup in order to avoid triggering this stipulation.

The same stricture did not apply to Sens. McCain and Graham, however. Sen. McCain had already announced that he favored ending American aid.

When asked by Egyptian reporters why he used the word “coup,” he replied in confusing fashion: “I’m not here to go through the dictionary. If it walks like a duck and quacks like a duck, it’s a duck.”

A prominent Egyptian journalist countered that McCain was “kharqa,” a word that could be translated as “clumsy,” “irresponsible,” “moronic” or “irrational.”

Yet while Sen. McCain’s penchant for “straight talk” occasionally strays past diplomatic niceties, he was right to deliver this fundamental warning to Egypt’s military regime — and to the civilians now rallying behind it:

Find a peaceful way out of this mess or risk the loss of U.S. aid.

The future of Egypt — and the Mideast — could depend on whether they listened.