That may be oversimplifying things a bit. Bush did carry Florida, after all. I think a greater part of the reason for their nervousness is that no one from the administration has really tried to explain it to them. This is a point that Bush needs to hammer over and over again, that he's not proposing to take away benefits from current retirees, and he needs to explain in relative detail what in fact he is proposing. Just as an example, instead of having each and every one of his radio addresses devoted to lofty talk about "spreading freedom around the world" or some such, he could devote a few such programs to explaining his plan, free from the meddling media middleman.
But regardless of whether retirees believe him, one thing they can't deny is that whatever money goes toward a private account for a young contributor will not go toward their own retirements. Hence, they would have to know that it won't make the slightest difference to them whether these young people are required to invest in some government-approved portfolio, or are allowed to do with their own money as they see fit.
But not because any silver hairs voted for him. Bush can hammer all he wants, maybe it will get through, but he will not change the political leaning of the AARP and they will send out a mailing to counter everything Bush says. And one mailing from someone they trust will outdo all the media Bush can buy.
And of course any money Bush pulls from the system and puts in the retirees personal accounts will require back up funding or program cutting. Both ideas are tough calls. If the programs are cut, then old timers can well believe that they will lose somewhere even if their SS check comes on time. Maybe what will be cut will be seniors bus passes for example. As far as back up funding, the best idea I have heard is to take out a loan to cover the lost funds. And retire the loan over the same length of time that the retirees are saving in their own accounts. At some time the government can stop mailing SS checks and let retirees withdraw from their own savings. (The ultimate plan anyway.) An at this time the government can switch SS check payouts to retire the notes that funded the program in the first place.