Simply give the order to attack
There's only over 65,000 Murrican troops in Europe, not nearly enough. Even in Germany they'd be outnumbered nearly 9 to 1, and that's where a third of them are stationed.
Few of those are infantry.
http://en.wikipedia.org/wiki/United_States_Air_Forces_in_EuropeA US first strike would be able to do devastating amounts of damage. It is, for example, 72 miles from
Fairford to London. That's 8 minutes for
B-2 bomber at nominal cruising speed.
And when you do get around to trying to repel them, remember that you're defend against...
not an outside invading force, but rather an enemy that is heavily entrenched with roughly 100 established, fortified military installations inside your countr(ies). Many of which are over 60 years old, and supplied with years worth of food and fuel. Worse, many of those installations are used by militaries from both sides.
For example:
http://en.wikipedia.org/wiki/List_of_Royal_Air_Force_stations"Royal Airforce" as in British military. From that link:
RAF Stations occupied by the United States Air Force * RAF Alconbury Cambridgeshire Occupied by the United States Air Force as an accommodation unit for personnel at RAF Molesworth.
* RAF Barford St John Oxfordshire Occupied by the United States Air Force as a communications station.
* RAF Croughton Northamptonshire Occupied by the United States Air Force as a communications station.
* RAF Fairford Gloucestershire Occupied by the United States Air Force.
* RAF Feltwell Norfolk United States Air Force support use.
* RAF Lakenheath Suffolk Occupied by the United States Air Force.
* RAF Menwith Hill North Yorkshire joint UK/US intelligence and communication site.
* RAF Mildenhall Suffolk Occupied by the United States Air Force.
* RAF Molesworth Cambridgeshire Occupied by the United States Air Force.
* RAF Welford Berkshire Occupied by the United States Air Force.
The enemy already occupies a large potion of your own military bases inside your own country. Do you bomb your own installations? Meanwhile, as you deal with the enemy within, your opponent himself is ~3600 miles away across an ocean. And no doubt bringing in reinforcements while you deal with the internal situation. A US fleet approaches from the west. Do you engage to attempt to stop them from landing, or do you deal with the 100-some bases that have already "landed?"
Tactically, logistically...the US has a crazy huge advantage out the gate.