The troubled market cleared a major hurdle to survival on Friday with provisional authorisation from the Department of Trade and Industry for its Equitas rescue plan.
Market sources say the deadline is now needed in order to complete computer processing for final liability statements to 34,000 names, which are due out by the end of May.
This weekend names, thousands of whom have been effectively bankrupted by pounds 8bn of losses from 1987-92, welcomed the DTI's move. But they warned Lloyd's would still have to come up with more than pounds 500m extra in compensation if action group members are to vote in Equitass' favour.
"Large groups of names are indicationg that the present settlement package is unacceptable. The worst hit names will have no hesitation in turning it down since they are better off continue litigating," said leading names representative Christopher Stockwell.
Mr Stockwell chairs the Lloyd's Names Associations' Working Party, an umbrella organisation for groups who have won a series of actions over negligence by Lloyd's agents and auditors.
The body sent out nearly 6,000 questionnaires canvassing opinion after Lloyd's sent out indicative statement of final bills for Equitas earlier this month. Around 50 per cent had replied and were nearly two to one against accepting the settlement as it stands, Mr Stockwell said.
Lloyd's is currently trying to secure a pounds 100m contribution from brokers, another pounds 200m from agents and pounds 200m from auditors to increase the compensation package.
Nicholas Verey of Lloyd's advisers Lazards is handling talks with the auditors, while Lloyd's chairman David Rowlands and chief executive Ron Sandler are liaising with agents and the London Insurance Brokers Committee.
"Everybody's playing poker, but the settlement can only increase. We know we can get pounds 2.8bn," a Lloyd's spokesman said. "But talk of up to pounds 4.5bn is not only unrealistic, it's stupid."
Mr Stockwell is currently proposing a 2 per cent levy on the future market to raise over pounds 4bn over 15 years, pounds 1bn of which could be released immediately to names.