It's not actual malpractice payouts that are driving up healthcare costs; the payouts actually account for very little in the industry overall. It's rather the medical over-testing that is routinely done in the name of avoiding those lawsuits. Over-testing accounts for a huge amount of expenditure in the health care industry every year, about $200 billion annually. But over-testing is done for lots of reasons, lots of times as a way for doctors to increase their revenues. However, a still significant percentage, about $60 billion of that $200 billion price tag in annual overteting is done in the name of "defensive medicine."
http://www.newsinferno.com/?p=43980
Another effect of the actual payouts, however, is to cause the price of medical malpractice insurance in the U.S. to spike for physicians--malpractice insurance premiums in the U.S. cost physicians about ten times what they do in other industrialized countries, and some of that cost surely is passed on to patients. (Not all of that cost differential is due to malpractice caps of course--these other countries have much lower costs both for patients and physicians across the board. But still, the difference is huge.)
I would support a very carefully crafted sort of tort reform, which would limit the amount of testing doctors would have to do in order to avoid lawsuits, and perhaps cap some claim amounts. But I think careful, detailed study would be required in order to design effective policy in this area.