I've observed that face saving behavior at all levels of society in America, but very few instances of people willing to point it out or discuss it, except sometimes to accuse people of 'covering up bad behavior'.

When you visit someone's house and they serve you food and ask if you liked it, unhesitatingly saying 'yes' is face saving and also just simple good manners.

When your boss makes a bad decision but you don't call them out in the next team meeting, and instead first bring it up in private, that is face saving. You're trying to avoid openly embarrassing someone and reducing their social standing.

In this case, face-saving just makes sense -- let's get a budget deal passed (which is in everyone's best interests), and then mollify the crazies in the base who refuse to see it that way.

I guess pointing out face-saving in the US is itself potentially embarrassing, because it implies that person might actually be worried about their social standing, which can itself negatively affect their social standing?