As far as I can tell, there is little to no evidence that converting social security to a means-tested benefits program would reduce political support for it.
I think that this theory relies on the single, albeit significant, case of welfare reform. Basically, federal welfare reform didn't just shift letters around when it turned AFDC into TANF, it really transformed the program's (dis)incentive structure. Conservatives (and centrists) think that this was a huge victory for responsible government; liberals are still smarting and grumbling over this one since they believe that you can't count the success of a program on the basis of how many people were eliminated from the rolls. (Indeed, for some of them it may not be a stretch to say that the more people a program serves, the better it is.)
Liberals have adopted a sort of dumbed down public choice. They believe that in order for a program to survive it either has to be (a) for the rich or (b) for the many. They think that the current version of SS is (ab) and so see means-testing as a poison pill.