Are malpractice suits responsible for high health care costs?

Probably not so much:

But are “frivolous lawsuits” the real cause of high health care costs? The short answer is no. Malpractice costs represent less than half of 1% (0.46 percent of total health care expenditures) and malpractice settlements have grown modestly with inflation. In fact, in states that have adopted caps on jury awards, doctors are prescribing too many aggressive and intensive treatments that increase costs, but don’t improve outcomes.

When Texas capped non economic medical malpractice damages to $250,000 in 2003, most conservatives argued that the reform would free doctors from having to prescribe unnecessary treatment. It didn’t happen. According to the Dartmouth research on disparities in health care spending, many Texan doctors are still prescribing aggressive treatments that don’t improve outcomes. In fact, as of 2006, Texas was still at the top of the list of high-spending states.

Here is the article, note that I don't agree with everything in there. That all said, most health care economists do agree that malpractice reform is probably a good idea, even if it is an overrated idea.