What specific evidence would people require to believe in God's existence?

I don't think it will be as dramatic as a collapse but rather a soft landing into mediocrity or irrelevance. What is already happening is that while it is still a top destination for foreign researchers, the US is losing its edge. The US education system does not produce enough home grown scientists to maintain its activities. Over time you will see scientists (already a mobile lot) moving to other countries or staying home rather than working in the US (already the case for stem cell research). The EU, China, India, Japan (if they are smart) will use the opportunity of a slipping committment to science by the US to take the lead. In fact, the current administrations outright hostility to science is sparking programs with silly names in Germany and Spain for example called "Brain Gain" which seeks to lure top talent back to their home countries or prevent them from leaving in the first place to the detriment of US science. The end result will be more discoveries, more patents, and more commercial activity outside the US...and a complete dependency of the US on foreign companies and entities as a source of pharmaceuticals, medicine, and general inovation. This dependency, like the collapse of the USSR will likely temper the fact that it has a huge weapons arsenal. In effect, an already small minority educated population in the US will become even smaller but will likely have a disproportionately high economic and social impact. The big problem is once you have a trend towards anti-science and willful scientific illiteracy it will be very hard to reverse. It is not something that the US will readily be able to reverse once it gains momentum. It will take generations while the US sits on the sidelines....we will become like our soccer team at the World Cup.