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.