The Minister for Health was accused of becoming "increasingly disconnected from the reality in the health service for which he holds responsibility".
During a debate on a Sinn Féin motion calling for Mr Martin's resignation, Fine Gael's health spokeswoman, Ms Olivia Mitchell, said he would be let off "too easily" if he resigned, that he should either "clear up the landmines" or let the electorate kick him out.
Ms Mitchell said the public believed the Minister "when he promised a world-class health service and he gave them shortages and service rationing of Soviet proportions.
"They believed him when he promised 200,000 extra medical cards and since then he has withdrawn 46,000.
"They believed him when he promised 3,000 extra beds and instead he closed 200 acute beds in Dublin. They believed him when he promised an IT strategy for the health service to be published in 2001. In 2004 they still don't have it.
"Someone said, if you can't measure it, you can't manage it, and that is certainly true of the health service.
"The Minister can't measure the number of patients, the numbers on waiting lists, the demand for services, the numbers of nurses or doctors or over 70s or deaths.
"He can't count, he can't cost, he can't screen effectively because he has no databases, he can't record information, he can't retrieve it, he has no patient identifier system and he can't do recall.."
Opening the debate, Sinn Fein's leader in the Dáil, Mr Caoimhghin O Caolain said that in 2002 "Fianna Fáil made a commitment to the electorate to permanently end waiting lists in our hospitals within two years. That promise becomes due on May 17th next.
"But there are still over 27,000 people on hospital waiting lists," a decrease of only 7 per cent since 2002. At current rates it would take more than 14 years to end the waiting lists, he said.
"There can be no confidence in a Minister and a Government with such a record on health, not only since 2002 but since 1997. This was their principal mandate from the people and they have failed."
But the Minister, in a sharp attack on Sinn Fein, said the party was "fine on the attack but doesn't feel it necessary to propose alternatives. They are the only party in this House that has never actually proposed an alternative Budget."
He criticised them for calling for "many billions in extra expenditure and they believe that I should resign because I have not provided it. They present an image of a country where no choices ever have to be made. To them, details are for other people."
He said the opposition would not acknowledge that the Government had delivered the largest sustained programme of real-terms increases in the history of the health service, and that 200,000 people were being treated in hospitals or that work was well under way on more than 80 per cent of the health strategy.
