Egyptian Army Commander and Defense Minister Abdul Fattah al-Sisi was faced in Cairo with that experts say was the largest human gathering in history -- somewhere between 17 and 30 million people -- demanding a chance to redo the 2011 revolution. A "mulligan," so to speak. The military responded by removing Morsi and announcing that it would not rule but rather manage a civilian-run transition.

The Obama administration should be pleased. Having made a mess of Egypt by abruptly withdrawing support from a longtime ally; by failing effectively to express its displeasure with 18 months of military rule that included the arrest of American and Egyptian NGO workers; and by accepting without comment Mohammad Morsi's power-grabs, his increasingly heavy-handed imposition of Sharia law, and violence against minorities, the U.S. is essentially getting its own "mulligan."

And indeed, the U.S. appears loath to deem the army ouster of Morsi a "coup," which would trigger an automatic cutoff of U.S. aid, more than 80 percent of which goes to the military. While never explicitly linked to the Egypt-Israel Peace Treaty of 1979, successive American governments have done their best not to tamper with the military figure, believing... well, believing what? Mainly, the United States appears to believe that we pay Egypt not to go to war against Israel and they'll march on Jerusalem if we stop.

This formulation was always a mistake, first because it ceded American leverage in advance. It also allowed Israel to be blamed over the years for the repression of the Egyptian people, and contributed to anti-Americanism based on the belief that the U.S. would tolerate anything that happened inside Egypt (the assassination of Anwar Sadat, corruption, sectarian violence) as long as Israel was protected. The truth is more complicated and might be made to serve American interests as much as Egyptian ones.

The Egyptian military is not champing at the bit to go to war with Israel, and is not held back by the American bribe -- um, aid. Furthermore, the generals are not sanguine about losing the United States as their chief supporter and do not see their future in the arms of Vladimir Putin. That is the definition of American leverage, but for it to be effective, the U.S. has to be willing to withhold as well as to pay.

Saudi Arabia, thrilled by the ouster of Morsi, has promised billions to the new Egyptian government, but that money will be needed to shore up the sinking civilian sector, buying food and fuel. Even if there was something left for the military, it isn't only the money. Egyptian military officers attend schools in the U.S. and partner with U.S. forces in counterterrorism and special operations exercises; the relationship is deep and valued by the Egyptians. The Saudis cannot replace that -- and neither can the Russians.

Despite 30 years of upgrades in weaponry and training, or because of them, the army has shown no interest in a) provoking Israel or b) helping Hamas. The military has no desire to put itself to the test against the IDF, and understands that the IDF isn't the enemy.

In Sinai over the past few years, weapons flowing westward from Iran and eastward from Libya have crossed the peninsula, and terrorism from international jihadist groups has increased. This is despite the efforts of the Egyptian military, not by collusion. The agreed-upon-with Israel increase in military sweeps, the additional equipment, and the operations close to the Israel-Egypt border have, according to Israel's Defense Minister, slowed smuggling. That fact that Islamists have been reported heading toward Sinai to fight the Egyptian military since the ouster of Morsi argues that this is a moment when American leverage would be at its peak.

Hamas, which had believed the election of Morsi would end its political and economic isolation and open a supply line from Egypt to Gaza, has been furious that the military has gone to great lengths to improve its performance and seal the Gaza/Egypt border. Contrary to popular opinion (including popular opinion in Washington) the military was uninterested in helping boost Hamas in its war against Israel, not only because of the American input, but also for two reasons entirely unrelated to Israel. First, Hamas is the Palestinian branch of the Muslim Brotherhood. Second, despite the fact that Palestinians are Sunni, Hamas is an outpost of Shiite Iran.

Among the regional players the Egyptian military most detests is Iran. This is another exploitable point of agreement with the United States, and a difference with Russia.

An article in the London Sunday Times recounted the growing closeness of Morsi and Mahmoud Ahmadinejad, including the latter's visit to Cairo in February. According to the article, Sisi believed Morsi was planning to replace him and was doubly worried when Ahmadinejad said he had offered to defend Egypt in the event of an attack. The Times cited the Egyptian weekly Al-Usbua, saying, "Sisi told the president the army objected to his remarks, which were an insult to the military and questioned its strength and its ability to face threats to the security of the country."

But even when Morsi took a position that irked the Iranians, he didn't do well with the military. Shortly before his ouster, Morsi had broken relations with Syrian President Bashaar Assad, giving a boost to the Islamist rebels fighting the government. While the military might have been pleased by Morsi's break with Iran on that issue, the specter of a Muslim Brotherhood or al-Nusra victory over a secular dictator was unappealing in the extreme.

The Egyptian military gave the people their "mulligan" and gave us another chance to get it right. This time, the administration should understand where the real power in Egypt lies, and not be afraid to use its considerable leverage to support the civilian demand for an accountable and transparent government. Ambassador Patterson should be brought home if for no other reason than that the Egyptian people believe she is President Obama's emissary to the Muslim Brotherhood, and the president should make it clear that participation in elections is a privilege reserved for those who ascribe to at least minimal standards of respect for individual civil liberties and rule of law. If President Obama can't or doesn't want to, if he prefers to pay what he thinks is bribe money, or chooses to cut off the funds to slap at the military or support the Brotherhood, the failures in Egypt will only multiply.

Shoshana Bryen is Senior Director of The Jewish Policy Center.