The worry here isn't that antibiotics will suddenly become useless and whenever anyone gets a bacterial infection they'll have no hope. The worry is that there will be a number of prevalent bacterial illnesses which can't be treated with antibiotics.
Currently antibiotics work for an overwhelming majority of bacterial illnesses, that's not going to change overnight. What will change is the idea that bacterial illnesses are trifles because they can be cured every time by antibiotics. A few diseases will emerge, more and more over time, that have much worse consequences than we are used to thinking about right now, but the rest will be the same.
I don't mean to underplay the threat, but if we keep pushing this rhetoric, people will discredit the threat when it turns out that 50 years later we're still using antibiotics for most illnesses that people actually get (because antibiotic-resistant strains are effectively quarantined). People will compare it with the "we're going to run out of oil" scare.