Some say they believe the market should be left unregulated with the addition of transparency to the system. Others say more strident steps should be taken, The New York Times reported Tuesday.
Credit default swaps are contracts that guarantee against debt securities going bad. American International Group, which accepted a $123 billion federal bailout last month, held $440 billion in swaps as it went under, the Times reported.
"If there's a sense that another AIG could happen," said Henry Hu, a law professor at the University of Texas.
The U.S. House of Representatives Financial Services Committee is conducting a hearing to review regulatory issues. Committee Chairman Barney Frank, D-Mass., took a swipe at those who prefer to leave the markets alone.
"I understand why my Republican colleagues do not want to examine our failure to regulate credit default swaps and the other fruits of their deregulatory push," Frank said in a statement.
"The results of that effort are now in -- a crisis that is sweeping the global economy and threatening tens of millions of working families."