Either the US meets Brussels demands, or the EU cuts off its nose in spite and throws gasoline on the anti-EU fire for member states that depend heavily on tourism from the US. Brilliant strategy, that.
Your governments aren't funding TV ads telling you that the future of your countries are American Trump supporters, and that you have to roll over and accept it. Or telling you that unemployed violent rednecks sipping Bud Light and waving the Confederate flag are quintessentially European, and that you are a racist to not want them in your neighborhood beating up your son and making increasingly inappropriate advances on your wife and daughter. And should these rednecks rape your young child, the courts don't them off with a slap on the wrist, because that's how they did it in rural America, and we need to be more accepting of other cultures. And your government certainly wouldn't fine you and send you to jail for hate speech if you complained about these rednecks and Trump supporters online.
Look at this very news article. Tourism from the US is an important industry for many EU member states, particularly the less wealthy. Visa requirements are going to have a horrible impact on the weaker member states. Brussels is more interested in playing political games with the US, increasing their own power, and stomping out nationalist seperatist movements (like trying to imprison Le Pen for posting ISIS videos) than it is with the well being of its member states.
Do not be surprised if desire to negotiate visa waivers bilaterally with the US to restore the tourism industry becomes another common refrain for populist, anti-EU candidates in a few years, albeit one a bit lower on the totem pole than other, more pressing dangers.