HEALTH Minister James Reilly's demands for the easing of health cuts due to population pressures have been rejected as tensions continue to mount in Government.
Ms Lynch was involved in "robust exchanges" at a cabinet sub-committee a fortnight ago, where Mr Kenny and Dr Reilly were present.
Tanaiste Eamon Gilmore was not at the meeting.
The Labour Party junior minister is understood to have strongly objected to the cutbacks in her area of disabilities and mental health.
Ms Lynch is believed to have stopped short of threatening to resign.
A source close to the Cork North-Central TD told the Irish Independent that she was "very unhappy" about some of the proposed health cuts.
"She made it clear in the discussions that she would not stand over certain measures which she felt would have a devastating impact on some of the country's most vulnerable people.
"A row did break out – but you have to realise that there are €666m worth of cuts at play so discussions are always going to be robust."
A spokesperson for Ms Lynch yesterday said she did not want to comment on what was a "private meeting".
Talks on the HSE Service Plan, setting out the €666m worth of the health cuts next year, are ongoing.
The €113m target from medical card savings has already been scaled back dramatically and alternative savings to cover the shortfall have to be found elsewhere.
Dr Reilly and the HSE have been pressing for some easing of the cuts, citing demographic pressures from the population changes and the need for improvements in maternity services.
To find the funds to cover the cost of these added spending pressures, the HSE claims the level of cuts next year will be closer to €1bn.
But it is understood this claim has been rejected as a "smokescreen" by government officials.
"That's just a smokescreen. That's a way of saying we need more money," a senior government source said.
Dr Reilly has repeatedly insisted the deficit for 2013 will be between €150m and €200m.
But there is speculation within coalition circles that the figure required in a Supplementary Estimate will be well above the €200m mark.
"Reilly has been absolutely consistent the overrun is going to be €200m," a source said.
The Cabinet is expected to sign off on the bailout on this year's health budget at its meeting tomorrow.
The Government was forced to dramatically scale back its planned cull of medical cards – leaving a black hole of more than €40m in further cuts to be found.
A new target for medical card probity will be set out, with estimates ranging from €55m to €70m – well down from the original €113m.
The real figure of what is actually achievable may be even lower, with a senior source suggesting it will be "less than half".
The €113m estimate was hugely controversial, as it appeared to have been created at the last minute and imposed on Health and the HSE in the run-up to Budget 2014.
The failure to reach the pre-set targets for savings from medical cards and pay mean cuts have to be found elsewhere.