No, they absolutely will not. I won't go into details but I can tell you from personal experience this is unequivocally false. The USA will in most cases do exactly nothing for their citizens in distress. Even the local US embassies will refuse to get involved in almost all cases.

You know who did get involved in our situation when I was with a group of mixed citizens from USA, UK, EU etc...? The UK and Denmark. France, the USA and Germany all did nothing at all.

This myth that the USA will save citizens from any situation needs to die. It's untrue and dangerous since it encourages Americans to do stupid things because they are convinced the Marines or Seals will come save them.