No. Payouts for damages and injuries caused by medical malpractice have gone up less than 1% a year since 1992. In that same 20 year period, healthcare costs overall have quadrupled, which means they have gone up 400%.  Read more in this excellent article by Michael Stratton on the Injury Board blog: 2011 National Malpractice Payouts Less Than .25% of Healthcare Costs.
Let's think about it: healthcare costs have gone up 400% in 20 years. Of that 400% less than 1% has to do with medical malpractice, which is breaching of a duty to take reasonable care by a doctor toward a patient. So the solution to escalating healthcare costs is to cap medical malpractice damages? That makes no sense and is utterly un-American. There are not supposed to be special privileges in this country.