The insurers are wary of how high the administration and Congress may try to push their industry's share of the losses. But they say they can readily agree to raising the attachment point, as the insurers say, to $500 million.
''Nobody in the industry cares whether the attachment point is $5 million or $500 million,'' said W.R. Berkley, the chief executive of the W.R. Berkley Corporation, a property casualty company. ''The issue is what do you do in an horrendous event where the industry doesn't have the capacity to respond.''
The insurers would prefer the continued coverage of commercial fleets and generally liability and to expand coverage to group life insurance, said Robert Rusbuldt, chief executive of the Independent Insurance Agents and Brokers of America. But, he said, ''I don't think issues like that are deal breakers.''
In its report arguing for an end to the government support, the Treasury said private reinsurance, which insurers buy to spread their risks, was increasingly available. But the insurers contend that they are only able to buy reinsurance to cover less than 20 percent of their current terrorism risk and that there would be less coverage without the government program.
''The bottom line is that there is no appetite now'' for private reinsurers to offer terrorism coverage, said Mr. Rusbuldt, especially after the bombings in London and, in 2004, in Madrid. ''What reinsurance company in its right mind is going to take on that sort of risk?'' he asked.