We'll have to wait and see, for the moment I think it's mere posturing coming from some European leaders.

To begin with, the European nuclear deterrent when it comes to keeping Russian on their toes is a joke compared to what the American have as part of their arsenal.

There is no European nuclear deterrent. The non-proliferation treaties bar any further countries from developing one. It would be a huge upheaval for even Germany or Italy, let alone the EU itself, to develop their own nuclear deterrent. (Not to mention politically impossible within Germany itself!)

The UK has a quasi-independent deterrent (we developed our own and then agreed to abandon it and buy the US option instead), but is not part of the EU any more.

The only true independent EU nuclear deterrent is France.

An under-appreciated aspect of the NATO/EU defence situation is that the US does not actually want the EU, or any of its constituent countries such as the former Axis powers, to become too capable. Or develop a local manufacturing capability that outsells the US one. The US actually prefers a weakish Europe defended by US troops to one strong enough not to need them and even to contemplate removing them.

The NPT could be exited. Germany is under a tougher bind with the 2+4 treaty, though.

Ultimately, Europe is capable of doing its own thing - US or not.

The US signaled pretty clearly that it cannot be relied upon so Europe will need to react (incl. on nuclear and other deterrence).