The affective/deliberative dichotomy could be the same as near/far from construal level theory. Hypotheses:

Giving someone a number of people that's been affected, like 3 million, triggers abstract processing and causes those people to be processed as socially distant. (Especially a large number--a small number, like 1, could cause you to start wondering about that particular person, causing them to be processed as socially close.)

Indeed, the person doesn't even need to be particularly identified, though it does help. In another experiment, people asked by researchers to make a donation to Habitat for Humanity were more likely to do so if they were told that the family "has been selected" rather than that they "will be selected" -- even though all other parts of the pitch were the same, and the participants got no information about who the families actually were5.

The family that "will be selected" is construed as being "far away" temporally, causing them to be processed as socially distant instead of socially close.

By the way, I recommend this review over Robin Hanson's writings for understanding near/far. Some of the stuff I've seen him write on near/far has made me think "no, that sounds wrong", although I haven't yet clarified my own interpretations enough to write them up. At least with a review you're getting it straight from the source.