The latest Government figures show more than 2000 people have opted out of receiving the cost of living payment.
On Monday, 970 people had opted out, meaning they had received a letter from IRD, but were not eligible. That number rose to 2227 on Tuesday.
The first $116 instalment of the payment was sent out on Monday, but some Kiwis based overseas say they have received it mistakenly.
National's finance spokesperson Nicola Willis has hit out at the scheme, calling it a "debacle" and "an absolute stuff-up".
The National Party has called for a review by the Auditor-General to investigate how much money has gone to ineligible Kiwis.
Revenue Minister David Parker said approximately 1% of the 2.1 million people receiving the payment would have been ineligible.
Parker admitted the Government knew some ineligible people would receive the money, but the alternative option of asking people to apply for the money was costlier and would see more people miss out.
The scheme has also attracted criticism from the Greens, who say beneficiaries should have received the payment.
Green MP Ricardo Menendez March says it's authentic of people choosing to opt out because they don't need the money, but tens of thousands of people have been overlooked.
"This just shows that the payment could have been better targeted to reach low income families working and on the benefit who desperately need support at this time," he said.
People who are receiving the Winter Energy Payment, many of whom are on a benefit are ineligible for the payment.
"We know that people on the benefit have been deeply impacted by the rise of inflation, and so we're calling on the Government to put in more interventions to genuinely support those who need it the most at this time."