"Can we panic now?" I can see why Europe and fans of NATO might be concerned that the US is reducing the number of army brigades based in Europe. The US has been seen as Europe's "pacifier" (using NATOsource's quote), assuring the Europeans that they don't have to worry about their neighbors but being far enough way not to threaten them much.
However, with most of Europe facing significant pressures to cut military budgets, who is the threat? Which countries will re-arm, worried about the neighbors, especially since the US is not withdrawing entirely from Europe? A couple of brigades, heaps of navy bases (US will be basing ships at Spanish ports to provide anti-missile defense), and air bases will continue to provide enough American forces in the region and enough infrastructure for the US to surge back if needed.
Perhaps the threat is "unresolved nationalism." I am not sure how American military power prevents the rise of nationalism. Not only am I a skeptic of about the impact of the EU on the good behavior of potentially irredentist European countries, but I am also a skeptic about NATO conditionality. NATO mattered in shaping the civil-military relations of the newly democratic countries, but other dynamics limited Hungary, Romanian and even Russian irredentism (like their own xenophobia). Until someone can tell me how two brigades in Europe would make a difference in the rise of nationalist politicians (oh crap, Orban and Fidesz came to power in Hungary before the reductions!), I will hope that that the move will save as many $$ as hoped for.
The funny thing is that NATO has been pretty happy with temporary presence as a means of providing assurance to Iceland and the Baltics. On a regular basis, an ally provides a number of planes to be based briefly in either locale, fly around, exercise, making sure the infrastructure is intact to support them. Given that the Baltics, more so than Iceland, are proximate to the biggest threats (Russia, of course) seem ok with this, why would the US need to keep two brigades in Europe to assure countries further away from the action (Germany, Italy, etc.)?
There would still be plenty of military-to-military interactions, exercises, schools, working groups, and such. So, NATO would still exist and still have the capability to do stuff in the region. The real threat to NATO is not so much moving some US assets further away from the scene but the cuts the allies are making in key areas. Eliminating one's armor entirely means there is no capacity to surge down the road, as all the folks experienced in armored warfare will be gone. Having only one squadron of planes means that one can only bomb Libya for six months. You get the picture.
So, it is kind of funny to see anyone in Europe complain that American economies in defense spending are problematic, given that European defense cuts are much more drastic (ask the Royal Navy). The US will continue to be spending huge amounts of money on defense, will still have a very large army, a very large air force (only threatened by the expensiveness of its latest planes), and the most powerful navy in the world. More of it will be dedicated to the Pacific, but they can come back to Europe when needed.
The problem is that Europe is a success story, and grand strategy requires balancing commitments and capabilities. There is some risk, but smart people face the risks and manage them, understanding the tradeoffs. Less aware folks ignore the risks and try to have everything (can Canada, for instance, really afford a modern air force, modern navy, and modern army? In a word, no).