It is a lie, of course. The rich actually pay a smaller percentage of their income in taxes (remember the 13% that Romney paid on over $21 million in income?), and so do corporations (some of whom don't pay any taxes even though they make billions in profit). And we are still waiting, decades later, for that magical trickle-down to start happening.
And this unfairness is not just in the income taxes paid (or not paid) by the rich and the corporations. The rich also pay a much, much smaller percentage of their income in FICA taxes (which go to support the Social Security program). While workers pay FICA taxes on 100% of their income, the rich pay those taxes on only a tiny portion of their income.
Now we are being told that Social Security is going broke, and that benefits for the elderly must be cut. That is another lie. Social Security is fully funded for another 25-30 years, and if nothing is done, will still be able to pay 80% of benefits after that. And if the rich paid the same percentage in FICA taxes that all workers pay, Social Security would be able to pay full benefits (and even raise those benefits) for perpetuity.
Social Security is not in financial trouble, and benefits do not need to be cut. But the rich do need to pay their fair share in FICA taxes -- just like all other Americans.