The BBC has learned that the police are seeking access to more than £200m of funding over five years to combat the threat from dissident republicans.
The government is believed to have sympathetically listened to the PSNI's argument.
The PSNI said it is in a unique position due to its role in countering national security threats.
The return of police checkpoints across NI is a public sign of police concerns about the threat from dissidents.
Police officers have been working 12-hour shifts for more than a week now as part of an ongoing operation.
The security services have also increased the resources they devote to tackling the threat.
This year more than 60 people have been charged with dissident offences.
But the attacks still keep coming, and the police fear more are on the way.
There have been 36 terrorist attacks against what are termed "national security targets" this year, and that is the highest annual total since dissident groups began their campaigns of violence.
Dissident numbers have also grown, and there are now believed to be around 600 people involved with the various groups.
The chief constable and his senior officers have publicly warned, a number of times in recent months, about the implications of significant cuts to the police budget.
Cheif Constable Matt Baggott told the policing board last month that the role of the PSNI was crucial for all aspects of life.
Mr Baggott said the political and economic well-being in Northern Ireland required them to be in a position to tackle the terrorist threat in the long term, as well as providing day to day policing.
That message was reinforced by Deputy Chief Constable Judith Gillespie at this month's meeting of the board.
"The chief constable is publicly on record on a number of occasions saying now is not the time to be cutting police resources," Ms Gillespie said.
But the serious discussions have taken place away from the glare of the cameras behind closed doors, with Mr Baggott urging the government to accept that the PSNI faces unique pressures.
My understanding is that the PSNI has said it can and will make efficiency savings, but the chief constable has also lobbied for access to more than £200m of special funding from the treasury reserve during the next five years to be used if he feels it is needed to combat the dissident threat.
The money would be used to improve the technology available for countering terrorism, to increase the amount of air support, and to recruit additional officers for close protection duties and guarding police stations.
The chief constable has pressed his case for access to additional funding in meetings with Prime Minister David Cameron in London, and in talks with Deputy Prime Minister Nick Clegg and the Home Secretary Teresa May, during visits to Northern Ireland this month.
The talks with the home secretary took place just days after she warned that the threat of a terrorist attack in Britain by dissident republicans had risen from moderate to substantial, meaning an attack is now regarded as a "strong possibility".
The police said they need access to additional funding to ensure they can contain and eventually reduce the threat.
While funding decisions are still being finalised, my understanding is that the government has signalled that it is sympathetic to the PSNI's argument.