The Washington Post has it correct, here:
According to then-assistant Secretary of State Elliot Abrams, Gingrich consistently voted for Reagan’s policies but was known more for his public criticism of the president. However, Reagan National Security Advisory Bud McFarlane, a Gingrich supporter, said Wednesday the congressman was “very influential” in the adoption of supply-side economics and the economic recovery.
On CSPAN Monday morning, Gingrich told Romney to stay out of fights “about a history he doesn’t understand.”