Fianna Fáil has called for measures to encourage younger customers to take out health insurance.
The Dáil is debating a private members' motion tonight and tomorrow calling for a reduction in costs.
It comes a day after new figures showed that 64,000 customers left the market in 2012.
The Dáil will also discuss the introduction of lifetime community rating, where people who wait until later in life to take out insurance would pay a higher rate than if they had joined at 25.
Fianna Fáil health spokesperson Billy Kelleher said the huge increase in the cost of premiums has led to thousands leaving private healthcare.
Mr Kelleher said those on the lower plans they will now have to subsidise those on the "Rolls Royce" plans.
He also said people have to choose whether to pay the gas or oil bill or have private health insurance.
In response, Minister for Health James Reilly said universal health insurance will be put in place and completed by the end of the Government's term in office.
Minister Reilly also said there are fewer patients on trolleys now that when Fianna Fáil was in government.
Sinn Féin's Caoimhghín Ó Caoláin said the health service is a two-tier system and Fianna Fáil was a supporter of the system.