Because of the way the Social Security program is funded -- through a payroll tax on workers along with an employer contribution -- many people believe there is an account for them at some government agency holding those contributions, or at least giving them credit for them, and that they will be able to collect their contributions when they retire. It's their money, collected from them monthly, and no matter their income level they have a right to get that money back when they retire. Try telling them that they don't. Even those people who understand that if their income is high enough they may not receive payments equal to all they put in get something back -- it's there for them no matter what -- and this increases support for the program.
But if we change the funding so that payments for Social Security come out of the general fund -- the money the government collects through taxes for all purposes -- and impose means testing (i.e. phase out the payments once income is high enough), the link between contributions and benefits would be broken and I fear support for the program would be broken as well. It would become another welfare program, and attacked. When programs are supported through the general fund there is competition for funding, there is never enough money to go around, and it wouldn't be long before the people in power, or with lots of influence over those in power (who don't really need Social Security in most cases) would argue that the money is best used elsewhere.
I am far from the first person to make this point:
Ross Douthat Argues that Social Security Would be Easier to Cut If It Were Changed from a Social Insurance Program to a Welfare Program, by Dean Baker: Ross Douthat argues convincingly that if we eliminated the link between contributions and benefits it would be much easier politically to cut Social Security. Of course he thinks ending the link would be a good idea for that reason, but his logic is certainly on the mark, people will more strongly protect benefits that they feel they have earned. ...
The payroll tax certainly can cover the program's expenses. In fact, had it not been for the upward redistribution of income over the last three decades, which nearly doubled the share of wage income going over the cap on taxable income, the projected 75-year shortfall would be about half of its current level.
Even with the current projected shortfall, if ordinary workers shared in projected productivity growth over the next three decades, a tax increase equal to 6 percent of their wage growth over this period would be sufficient to make the program fully solvent. The problem is clearly the policies that led to the upward redistribution of income..., not Social Security.
It is worth pointing out that when Douthat proposes "means-testing for wealthier beneficiaries," his notion of wealthy means school teachers and firefighters, not Bill Gates and Mitt Romney. ...
Peggy Noonan said today that Republicans will accept tax increases if there is significant entitlement reform. Assuming she can be believed (a rather heroic assumption), and that she speaks for a significant portion of the Republican Party in saying this (which is probably true, so I'm a bit less embarrassed about quoting her), it's clear that Republicans are going to demand cuts to programs like Social Security as a condition of raising taxes.
Democrats need to remember who won the election, and that despite their act to the contrary, the Republicans are not the ones calling the shots at this point. Democrats have considerable leverage, and they need to use it to protect programs their core constituency values highly. Social Security is at the top of the list.