Though it might not represent the satisfactory answer you are looking for, I would argue the “big hammer” you seek lies with the science itself. We’ve 1) long known the properties of CO2 and water vapor and their affects on climate, and 2) more relatively recently, we’ve known the excess of global CO2 today is unprecedented and that it is inseperably linked to anthropogenic GHG production.

Consider the interplay between water vapor and CO2, the two major contributors to the greenhouse effect. As you may know, CO2 makes up but a small fraction of the Earth’s atmosphere relative to water vapor. CO2 accounts for only one in every 4000 molecules in the air, while water vapor accounts for one in every 20. Secondly, CO2 absorbs only a quarter as much energy from sunlight as water vapor, molecule for molecule. This seems to suggest that water vapor is responsible for the majority of atmospheric heating.

However, altitude is a core consideration here. Water vapor concentration levels are inversely proportional to altitude, unlike CO2. Whereas water vapor concentrations taper off very quickly with altitude, CO2, methane and other greenhouse gaeses do not. CO2 retains the same concentration level in the upper troposphere as on the surface. The upper troposphere is the most salient variable here as that is where heat is released into space. Thus the amount of non-water vapor GHGes determines how much heat is trapped in the Earth’s carbon cycle.

Perhaps the most convincing evidence is the simultaneous warming occurring in both the Northern and Southern hemispheres, something that has not been observed in the last 20,000 years. Based on all of our historical data, hemispheric relationships are consistently discordant. That is, when temperatures rise in one hemisphere, they fall or remain unchanged in the other. Since the Industrial Revolution, however, both regions have been monotonically warming. Human carbonization best explains why this is occurring. Make no mistake; our current trend is an unnatural outlier.

http://esciencenews.com/articles/2011/10/21/no.simultaneous.warming.northern.and.southern.hemispheres.a.result.climate.change.20000.years

But what has climate science got that is as equivalent and irrefutable like a sample of moon rock that turns out to be green cheese? Is climate science in possession of evidence so irrefutable? A sample of moon green cheese is the big hammer, the big proof. I don’t think climate science has that big hammer. They have lots of corroborative evidence but no big hammer, no big proof which slams the case shut, like an actual piece of moon rock green cheese. That’s the kind of evidence that climate skeptics are looking for, not merely a ‘preponderance of evidence’ , they are looking for the big hammer, that chunk of green cheese.

A few months ago it was proved that there has been a warming trend over the last 50 years, based on analysis of ground based temperature records. But the skeptics were not impressed, they said that a warming trend is merely evidence that the climate changes, it is not evidence that CO2 is the cause. That wasn’t the big hammer needed to convince the skeptics, but it was more than enough for the believers.

So what is the big hammer? I really do not know. Where is that green cheese.