My first guess was promises of reciprocality, but that seems like a hard sell to countries without a meaningful IP economy.
I can't imagine it being enforced with bullets. There's no way to rally troops to defend a copyright that doesn't make you look like the bad guy.
Was it smuggled in as part of other trade agreements? (If you want to sell us $resource_you_actually_have, you have to also agree to worship the almighty circled C?)
Today though pretty much everything in the Berne Convention is part of agreements you have to implement to join the World Trade Organisation, which is a pretty big motivation to abide by it.
However, the US probably has enough weight that other countries would just have to adapt if it wanted a shorter term, but at present there's no evidence of much political efforts for one.