It would seem so, yes. But in fact they need to convince the US government that the issue is worth exercising some pressure on the EU. And the USA has a wide array of options here.

When Chelsea Manning released her cables, there were too many of them for any journalist to read or even glance not to mention understanding what is going on. But I spent several weeks grepping and reading many fragments. My conclusion is that the US government cares a lot about their business in other countries, especially in Europe. Ambassadors reported a great deal about how things are going for American companies, what threats are (like European citizens realizing what's better for them), how to neutralize them and so on.

If the US was able to exert sufficient influence on the Eu, the trade war that the US itself started in 2005 would not reach such a point in which the Eu basically placed a kick in the balls of the US tech monopolies.

Which should never have happened and those companies should have never been let to dominate the Internet and everyone's lives to this extent. Especially considering how they are private tyrannies that decide whatever is the best for them, not their users.