You should see Svensmark's 2012 paper published by the Royal Astronomical Society.

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I have it and have read a good chunk of it (namely his findings, explanations, and caveats). A few quick things:
1. He's talking about impacts from GCRs assoicated with nearby supernovae
2. He's linking exceptional levels of GCRs on account of nearby supernovae to coolings that took place over long time-scales ("sudden" in geological time)
3. He acknowledges a recent "divergence" (speculating that it might have to do with C4 plants, which have an extra carbon atom)
4. He does not argue against an increase in CO2 offsetting the impact of GCRs driven by a nearby supernova, much less the much lower level absent such supernovae. On that matter, he writes:
Other processes might in principle counter a cooling of the climate by negative feedback. For example, if a cooling reduces the loss of CO2 to geochemical weathering, which could lead to a build-up of CO2 if other sinks and sources of CO2 remain constant, and so dampen or reverse the cooling (Donnadieu, Godd´eris & Bouttes 2009).
In effect, Svensmark is not arguing against the Greenhouse Effect associated with CO2. In fact, he's suggesting that the GCR impact exists alongside other climate drivers, including CO2. He writes of the combination of drivers, "The net impact of such processes will eventually have to be resolved by estimating the forcing of the individual processes and incorporating them in a multidisciplinary numerical model beyond the scope of this paper."
In sum, a similar impact to the one he described related to an increase in CO2 could occur if some other mechanism (natural and/or anthropogenic) led to increases in CO2 emissions to the point where emissions exceeded absorption and atmospheric CO2 increased. Currently, that's where things stand and atmospheric CO2 is approaching 400 PPM and will probably reach or exceed it before the end of this decade (annual average).
As he acknowledges other drivers and suggests that additional work would be required to find the "net impact," one cannot automatically assume that his conclusion debunks AGW nor that a nearby supernova would necessarily produce the same kind of cooling that has occurred in the past given those other drivers, particularly CO2 (that he singled out as posing a risk of damping or reversing a GCR-driven cooling). In the end, he contributes a factor that could have a climatic impact (he believes it has in the past given his data), but does not propose that his work offers an alternative explanation to AGW.