In comments on my first post, Marty Gilens alerts me to errors in the 2008 ANES data file that involve the spending variables that I used (noted here on their webpage). It is my fault for not having seen this. I have downloaded the corrected variables and revised the graph, which is above.
The story changes with regard to two programs—welfare and foreign aid—both of which are far less popular than in the original graph. About 49% of conservatives want to cut or eliminate foreign aid; 35% want to cut or eliminate welfare. The other programs, however, are again quite popular. The average percentage of conservatives who want to increase spending is unchanged: about 54%.
Thus, the original point of the Salon piece (to which corrections are forthcoming) remains: despite opposition to government spending in general, conservatives do not advocate reductions in government spending on particular programs.
Update: the corrected Salon piece is here.