Is there any accuracy to this?
The Real Reagan Economic Record: Responsible and Successful Fiscal Policy
http://www.heritage.org/research/reports/2001/03/the-real-reagan-economic-record
As I recall, Reagan lowered tax rates but also eliminated some deductions. For some people that might have meant a tax increase. The idea was to simplify the tax code, but it never really happened to any substantial degree.
One of Reagan's big things was to rebuild the military during his two terms (esp. the Navy) -- something that RP probably did not approve of. The democrats knew that they could stick all kinds of stuff into a military spending bill (which they did), and Reagan would probably still sign it.