The National Party is calling for a broader investigation into whether the government's most senior ministers have orchestrated a smear campaign against the opposition.
Finance Minister Grant Robertson is under pressure over whether he acted quickly enough to correct allegations National had hacked the Treasury website.
Police initially investigated how National obtained secret Budget details, but quickly concluded nothing illegal had happened.
The minister responsible for the Government Communications Security Bureau (GCSB), Andrew Little, received a call from the spy agency's head Andrew Hampton to say no hack had occurred but is remaining secret squirrel on when he passed that on to Mr Robertson.
The State Services Commission is investigating the Treasury's actions but cannot legally look at the role of government ministers in the aftermath.
A furious National Party has called for the resignation of both Mr Robertson, and Treasury secretary Gabriel Makhlouf for smearing its name.
National is adamant it did nothing illegal to obtain secret Budget information, as it was done by a search of the Treasury website.
Deputy leader Paula Bennett said government ministers needed to come clean.
"We in the opposition will not let this lay, it actually goes to the heart of a government and whether or not they're covering something up. The issue itself is almost now secondary to actually the cover-up of a mistake that was made and everyone's ducking for cover,'' Mrs Bennett said.
The sorry saga of hack-gate started with Mr Makhlouf crying foul nearly a fortnight ago and calling in the police after saying there had been a "deliberate and systematic hack" of Treasury's systems.
Shortly after, Mr Robertson issued a statement linking the National Party to so-called hacked information.
Mr Little was contacted by the GCSB that night and was told no such hack had taken place.
"I had a briefing from Andrew Hampton, there's no question about that. I don't want to go into anymore detail because I think it's unfair on the State Services Commission and others who the State Services is investigating."
Mr Little said the State Services Commission can have whatever information they want from the government.
"The State Services Commission knows what it is they're investigating. They'll know what information they need and whatever they information they need whether from officials or ministers or their offices, they will get.''
But the investigation is looking only into Mr Makhlouf's claim Treasury's website had been hacked, the advice he gave the Finance Minister, and his decision to contact the police.
The State Services Commissioner Peter Hughes has informed Mrs Bennett investigations into the actions of ministers are - quote - "beyond his jurisdiction."
Mrs Bennett said that's not good enough.
"The prime minister could call a wider inquiry if she wanted to but the SSC, it is very clear in the Cabinet manual and their terms of reference, that they cannot cover ministers and Andrew Little needs to tell what he knew, when and whom he passed that information onto.''
Once the allegations of a hack were made it was 18 hours before Mr Robertson started to refer to it as an "unauthorised access''.
He denies making any accusations against National.
Mr Robertson also refuses to say when exactly he knew it was not a hack.
"That evolved over time and I'm sure that timeline will come out as we go but I certainly did not know about it before I put my statement out,'' he said last week.
Likewise, the prime minister said she's already publicly stated when she was told Treasury had taken the matter to the police and will not discuss any other conversations between ministers while the investigation is underway.
Mrs Bennett said the government can expect to be pushed on that.
"Well they can't hide behind the SSC investigation because it simply doesn't cover them, so as such we'll be drilling into the detail of who knew what when and I would hope the House upstands its standing orders and as such we get answers,'' Mrs Bennett said.
The GCSB, Treasury and the State Services Commission will not comment further while the investigation is under way.