That is what Rush repeats constantly, but it isn't what Reagan's own economists write in their memoirs. In fact Martin Anderson makes the point of addressing and denying this very claim. Revenues did drop when rates were cut, which is why President Reagan wanted spending cuts from Tip O'Neill. When O'Neill reneged on the cuts, deficits exploded and there was a tax increase in 1982.
Lawrence Lindsey, Dubya's first economic advisor, did a comprehensive analysis of the effect of the Reagan tax cuts when he was at Harvard, a study published as The Growth Experiment. You can't simply subtract total tax revenues of 1980 from those of 1988 and claim the difference is all attributable to the tax cuts. You have to account for the normal business cycle, demand side effects of deficit spending, mean growth rate of the economy, and host of factors that are addressed by regression analysis. The dynamic effect of the cuts recouped 2/3 of the revenue loss predicted by a static analysis of the tax cuts. But the point of the Reagan program was to grow the economy, not to grow tax receipts, and Reaganomics succeeded.