If you really want to crunch some numbers on this, you could check the U.S. Census Bureau web site. They have published tons of information on this. Here is a table of household income distribution over time.
They show the top 5% of households going from reporting 14.9% of income in 1975 to 20.3% in 1999. However, it's possible that as much as half of that increase could be due to changes in measurement methods that took place around 1993.
My own take on this is that wealthy households are indeed paying a significantly higher share of federal income taxes than they used to. I expect the wealthy will survive. Still, it's useful to keep in mind when you hear the next Democratic campaign speech.