I recently traveled with my young son, who is a Japanese and American dual national, from Japan to the USA. I realized shortly before the trip that his American passport had expired and there was no time to get him a new one. Knowing that Americans are supposed to enter/leave the USA on their American passports, I was thrown into a bit of a panic.
After calling the US Embassy in Tokyo and determining that there was, indeed, not enough time to get even an emergency temporary passport, I called Japan Airlines (JAL), with whom we were scheduled to fly. The lady on the phone at JAL didn't seem at all worried about the situation, which I explained in full. She took my son's full Japan passport details and told us to get an ESTA. I was a little worried about the ESTA because getting one required us to lie on the online application where it asks if you have another citizenship. In order to get one, we had to answer "no" but the ESTA was immediately confirmed and we never heard anything more about it.
I searched this forum and on found
this post on a related topic. The replies by GUWonder were particularly useful and completely accurate. He posted a link to
this page which set my mind at ease (I printed it out and brought it with us when we flew). The gist of that page, from the US Customs and Border Patrol Agency is this: In a true emergency, when a US dual national cannot obtain an American passport, they can travel to/from the US with their second passport. Here is the relevant passage: "If you have a true emergency, and are unable to obtain a U.S. Passport before your travels and have only a VWP-eligible country's passport, then you will have to file with ESTA to use that passport to travel to the U.S., and you will have to use the non-resident queue when arriving at the U.S. airport using the foreign passport."
Despite finding this, I was pretty nervous on the outgoing leg. When we checked in at Narita, I was worried that the girl at the counter would ask to see my son's American passport, but she did not. Then, I sweated it out all the way to Logan, but was relieved to see that Americans and ESTA holders clear immigration at automated kiosks, which do not ask awkward questions. Those kiosks spit out papers that you carry to a final interview with a customs official, who did not ask any awkward questions either (though I suppose she could have - I reckon this was the final hurdle). And, upon checking in at Logan to fly back to Japan, they only asked to see my son's Japanese passport, so no worries there.
So, thanks to the good people on this forum, GUWonder in particular, I did not cancel my trip in order to renew my son's American passport and I was able to travel with something approaching confidence.
To sum up: If you are an American dual national and you must enter the US on your second passport, it appears that you can do it as long as you are from a VWP-eligible country. Just make sure that you can satisfactorily prove that you were truly unable to get a valid American passport and make sure to get an ESTA with your second passport. As I did, I'd suggest checking with your airline in advance and brining a printout of the above-mentioned page from US Customs and Border Patrol. Thanks FT people!