The Illinois House has rejected a Democratic plan that would have given state regulators more oversight of doctors and insurers, discouraged unmerited lawsuits and offered $50 million in state money to help doctors pay high insurance premiums. There is another medical malpractice bill, backed largely by Republicans and doctors, still pending in a Senate committee, though it will probably not come up for a vote. In some cases, doctors are paying three or four times more for coverage than they did a year ago, and specialists such as heart surgeons can now be hard to find in certain parts of the state. Critics bashed the idea of providing $50 million to help pay insurance costs, with some saying it would do nothing to fix the problem. The money would have come from a half-percent tax increase on health insurance companies.