Openate - thanks for posting this. I don't remember seeing this issue discussed on the forum and I've been here for about 10 years.
My story is a little different. I was visiting Chicago, my home town, and my passport got lost (2 years later it was found and it was not my fault :-). I discovered the loss the day before my flight home to Tel Aviv. British Air was very helpful and the kind agent was able to find a flight for me at the same fare, 9 days aways, for the minor $75 change fee only (earlier flights would have cost me hundreds more). Since I wasn't sure I'd have a passport, she put the reservation on hold and I had 2 days to confirm. I then called the Chicago Passport Agency. They have limited hours on limited days. They would give me an appointment for 2 days later to apply for an emergency replacement passport. They said I had to bring a valid flight ticket for the date I wanted to fly before I could apply to get the passport, but they would absolutely not commit to issuing it in that time. I would also have to provide proof of citizenship, either a birth certificate or a "Fully-valid, undamaged U.S. passport (can be expired)". So I made an appointment and went to Cook County to get a notarized copy of my birth certificate. Well, that was a non-starter. I officially changed my name after moving to Israel, so there was no way the county would give it to me, and anyway I would have also had to provide the documents certifying the name change, which I don't normally travel with.
Happily, I am also an Israeli citizen (my Israeli passport was in the same place as the US one, of course). I got an appointment for the next morning at the Israeli consulate. I showed them my Israeli driver's license, they found me in their database and told me they would issue a "laissez-passe" which would allow me to transit at London Heathrow and enter Israel. The only drawback was that they were skeptical that I'd be able to enter and leave LHR, as I had planned to spend my full day layover with a friend who lives in London. Instead I had many hours to explore every nook and cranny of Terminal 5.
I don't know what the protocols are at US embassies and consulates in Europe. In Israel, you have to make an appointment for any US citizen services. It takes several days wait. Then you spend at least a couple of hours waiting. In the wake of 9/11 all passport requests are sent to the US (embassies used to issue passports), so the process can take a couple of weeks or more.