The Breaux-Thomas report Gingrich referred to was the end result of a bipartisan commission on Medicare reform conducted in 1999. A central component of the Breaux-Thomas proposal was, you guessed it, a plan to convert Medicare to a premium-support model with the federal government subsidizing, and regulating, the purchase of private health insurance plans. While certain aspects of Ryan’s plan differ from Breaux-Thomas, particularly in the area of cost controls, the underlying architecture is very similar. (Sen. John Breaux was a Democrat, after all.)
Gingrich, based on his comments quoted above, was clearly supportive of the Breaux-Thomas framework, and in fact earlier in the same speech called the plan “a good first step”, while advocating for more direct financial responsibility on the part of everyone within the healthcare system.