Maybe it's because the sponsor of the bill has been sued multiple times himself for medical malpractice...the NY Times and Mother Jones has the full story:
Case in point is one of the very congressmen sponsoring the bill, Rep. Phil Gingrey (R-Ga.). In 2007, the New York Times reports, Gingrey, who is a doctor, settled a lawsuit for $500,000 in a case involving a pregnant woman whose appendicitis Gingrey and others failed to diagnose. Her appendix burst, causing a massive infection that left her unborn child dead and the woman partially disabled after she suffered a stroke as a result.
That wasn't the only time Gingrey has been sued. The Times writes:
In a pretrial deposition, Dr. Gingrey testified that he had been sued at least three other times over malpractice during his long career. In one case, a jury found against him; in another case, there was a settlement; and in another case, the patient dropped the action, he testified.
It's no suprise that the doctors who get sued a lot are the ones who complain the loudest about "frivolous" lawsuits. But the case against Gingrey seems anything but frivolous. But it's just those sorts of serious cases that Gingrey's bill would restrict. And far from saving money, the bill would simply shift the cost of negligent medicine from the doctors and their insurance companies to the taxpayers through Medicaid and other disability programs. Private health insurers also can often recoup their costs for covering malpractice injuries through those lawsuits. Catastrophic injuries like the one suffered by Gingrey's patient profiled in the Times tend to bankrupt people, leaving them reliant on government health care, and the costs can be significant.