That's not a logical reason. In fact, it's exactly the problem. It becomes ideological; here's how that logic works:
Liberals - we can't support SS privatization, because conservatives support it.
Conservatives - we can't support slashing the defense budget, because liberals support it.
Here's a compromise - liberals give in to privatization, and conservatives agree to slash defense. We can make it 1 bill, and save the U.S. economy.
Ike didn't realize that SS was unsustainable in the '50's. The same group that - when polled- says they don't think they'll have SS when they retire, is the same group that is opposed to privatization. It's non-sensical.