Ministers want to reject Nphet's advice for Level 5 restrictions, but accept more measures will have to b introduced to curb the spread of Covid-19 in the coming weeks.
There is a growing belief that the Cabinet will again shoot down Nphet's call for the highest level of coronavirus regulations and instead introduce Level 4 restrictions.
However, senior figures in the two main government parties say it is inevitable that tougher countrywide lockdown measures will be introduced in the coming days.
Ministers are eager to stick to the Living with Covid-19 Plan, which allows for a step-by-step approach to introducing new rules. This would mean moving to Level 4 before Level 5.
The main differences between the two levels is that, under the highest level of restrictions, pubs and restaurants can only provide takeaway and deliveries and people cannot travel farther than 5km from their home.
"The reality is the next few weeks will be very restrictive and you can call it what you want, but things are going to be bad," one Cabinet minister said.
The minister said the Cabinet may "modify" the Level 5 restrictions so they are not as severe as set out to allow people to travel farther from home.
"It would be essentially Level 4, but we could call it Level 5," the minister said.
Another senior minister said: "The safest course politically is to accept the advice as numbers are likely to rise for the next few weeks in any scenario, but I don't know if that is the right thing to do."
A Cabinet colleague added: "I would be against moving to Level 5 straight away. We need to move up the levels as set out in the plan."
There is frustration in the Cabinet over the lack of an exit strategy in the Nphet's plan.
A government source said Nphet has not set out how a six-week lockdown should end.
Yesterday, Taoiseach Micheál Martin said he will give the Nphet proposal "very detailed consideration" ahead of a Cabi- net committee meeting on Covid-19 today.
Tánaiste Leo Varadkar said the Government will consider the public health advice along with economic and social factors before reaching any decision when they meet.
"It has to take into account a number of things - obviously the public health objectives around saving lives and preventing transmission of the virus, but also the impact on mental health, general health, impact on disability services, on education, on society on jobs, and that's what we will do," Mr Varadkar said.
It comes after the Government introduced Level 4 restrictions for Cavan, Monaghan and Donegal on Wednesday and a nationwide ban on household visits.
At the meeting, Higher Education Minister Simon Harris suggested the entire country should be put on Level 4.
Other ministers are understood to have questioned why a national Covid-19 communication campaign similar to road safety advertising has yet to be introduced.
There is an expectation that a Cabinet meeting may be called this weekend to discuss the introduction of new regulations.
This will be decided after today's Cabinet sub-committee meeting.
Meanwhile, Minister of State Patrick O'Donovan said the Government cannot be blamed for the spread of the virus.
"Level 5 or Level 6 or Level 7 - it doesn't matter what level we go to, unless we all act responsibly in this," he said.
"The Government responds to trends in which the virus presents itself and tries to do as much as it can.
"We all need to work collectively to reduce the spread, but the Government does not have the cure for this.
"Government can't combat this on its own. We can advise, we can put the tools in place and we can put the money in place, but the only people that can suppress the virus are the Irish people."
Fine Gael TD Alan Farrell tweeted: "It appears that Nphet are briefing the media again - ahead of its primary function of advising the Cabinet - causing speculation and worry.
"If this leaking continues, serious questions must be asked as to whether or not the body is fit for purpose in its current form."
Fianna Fáil TD Barry Cowen opposed Level 5, urging: "Retain Level 3, work with it, implement it, adhere to it. Moving to 4 or 5 is running and hiding from Covid."