7. "Republicans haven't cut Medicare. cut it by $500 billion, and he cut it to pay for Obamacare." -April 11, 2012, in an interview with Fox News
Romney's comment here lacks important context. Under the health care law, Medicare spending will continue to grow. What Romney meant when he said that Obama "cut" Medicare is that the Affordable Care Act reduces the amount spent on the program by $500 billion over a 10-year period. Moreover, as the conservative Heritage Foundation points out, the health care law raises the payroll tax for Medicare for certain tax brackets, which would bolster the program.
In addition, Romney himself has called Medicare "inefficient," and (as HuffPost's Sam Stein points out) a large portion of the $500 billion would come out of Medicare Advantage, which has had trouble controlling costs in the past.
Romney's statement that "Republicans haven't cut Medicare" suggests the GOP wants to preserve the program. In fact, Rep. Paul Ryan's (R-Wis.) proposed budget, which Romney has endorsed, would fundamentally alter Medicare by giving seniors the choice to buy private insurance instead.
Critics of Ryan's plan have noted that it would allow insurance companies to hand pick healthier patients and would merely shift costs onto the beneficiaries.