Screenshot of Egyptian state TV video of Defense Minister al-Sissi announcing the end of Morsi's presidency. (YouTube)

It only took a few hours after the Egyptian military deposed President Mohamed Morsi on July 3, for Washington to launch into two debates. First, should the United States follow a law requiring it to cut foreign aid to countries in which a coup unseats a democratically elected leader? And, second, is it possible that the coup was actually a good thing for Egypt?

It's not clear that either debate will ever be totally settled, but there's enough uncertainty on both that the Obama administration seems to have decided against calling what happened a coup. Doing so would, unless President Obama secured a special waiver, require cutting the foreign aid that helps prop up Egypt's struggling economy and buys the United States leverage there. And it would also seem likely to confirm many Egyptians' suspicions that the U.S. was quietly backing Morsi and the Muslim Brotherhood in an effort to suppress Egyptian popular will. And it's not just the White House. The two leaders of a key Congressional committee quickly put out a statement that, while not exactly endorsing the coup as a great idea, clearly signaled that they would not oppose it.

The thinking seems to be, as State Department spokeswoman Jen Psaki put it while deflecting increasingly frustrated questions about the U.S. refusal to take a position, "Taking a side isn't in Egypt's interests."

But there's one way in which taking sides could be very much in Egypt's interests: the transition to democracy. It's worth remembering that way, way back in mid-2011, we were at a very similar place: the military was in charge and the U.S. was leaning on it to set elections, get a constitution approved and hand power over to a civilian, democratic government. That transition, for a multitude of reasons, clearly did not really work out the way that anyone wanted.

How the United States and other international groups respond to the July 3 coup could play a highly significant role on how this political transition unfolds, what sort of government it leads to and when. In this respect, at least, the best thing for Egypt might be calling it a coup.

According to research by political scientist Clayton Thyne, a professor at the University of Kentucky who summarized his findings at the blog The Monkey Cage, coup governments tend to hang on to power longer and transition to democracy more slowly when they have support from foreign states and international organizations. What he terms "negative support" – for example, by labeling the military takeover as a coup – actually seems to make a transition to democracy faster and more likely.

Thyne examined 205 coups from 1951 to 2004, gauging in each case whether the coup government was supported by other countries and by international organizations. Coup governments that got positive support from other countries tended to hang around another 3.34 years on average. Positive support from international organizations got them 1.31 more years in power. Coup governments supported by both foreign states and international organizations enjoyed an average 2.21 more years in power.

The African Union, one of the international organizations that might condemn Egypt's coup, has suspended the government's membership, but the biggest player here, the United States, seems to be sending messages of implicit support, or at least an implied "we're looking the other way while you sort this out."

The Egyptian military does not seem terribly interested in directly ruling Egypt for long and is making noise about setting elections. But the way that the military rules, however brief its tenure, could play an enormous role in determining whether Egypt successfully transitions to democracy this time around. Thyne writes, "Without strong international pressure in support of democracy, the military in Egypt essentially has a blank check to do whatever they want with the state. We’re quickly seeing this play out with the crackdown of supporters of the previous government."

He's right: the military is cracking down hard on the Muslim Brotherhood, arresting top members, keeping Morsi under guard and generally signaling to the the group, which has a broad base of popular support, that they're not welcome in Egyptian politics anymore. That could be hugely detrimental to Egypt's political transition, making national reconciliation less likely and the Brotherhood's opposition to the next government more likely. A group as large and influential as the Muslim Brotherhood has to be on board with Egyptian democracy in order for it to work; recall how quickly Morsi's rule disintegrated when non-Islamists realized they had no place in the government and so took to the streets calling for its downfall.

For that cycle to repeat, yet again, wouldn't serve Egyptian interests and it wouldn't serve American interests. That's why, per Thyne's research, the United States and other international actors could potentially play a significant role in accelerating Egypt's transition to democracy and moderating the military's rule by criticizing the coup that brought it to power. That doesn't necessarily make it a good idea to reduce aid to Egypt, nor does it minimize the damage that Morsi himself was causing to his country. And it certainly doesn't make it a good idea to cut aid off entirely and risk ending what's been, overall, a rocky but important U.S.-Egypt partnership. Still, sometimes a true friend is the one who tells you things you don't want to hear.