"If he's not confident that it's not the right thing to do, then he as the minister has the power to say 'You shouldn't do that'. They wouldn't have made that announcement without his blessing."
Mr Woodhouse yesterday ordered a review of the police's public messaging on road safety over the summer period, saying it was important that campaigns were "understandable and unambiguous".
The campaign had been widely criticised by the public and agencies.
Police Commissioner Mike Bush had warned drivers that the 4km/h tolerance above the speed limit was no longer in place and motorists could be ticketed for driving 1km/h over the speed limit. But he also said individual officers would decide whether to issue tickets for drivers caught driving only a small amount over the limit.
Mr Little said the review looked "a bit flakey. It looks to me like he's now looking for a way out and ducking responsibility for a judgment that he took a couple of months ago."
Mr Woodhouse stood by the zero tolerance policy but said the police's communication of the policy had been confusing and had created "unnecessary anxiety" among motorists.
New Zealand First MP Ron Mark has called for any tickets issued to people driving slightly over the limit to be refunded.
Mr Woodhouse said this was "patent nonsense" and preliminary data showed the number of speeding tickets for people driving at 101km/h to 104km/h were "very, very low".
The results of the review were expected by the end of February and any potential changes would be in place before the Easter holiday.
Seventeen people were killed on the roads over the Christmas-New Year, more than double the 2013-14 toll.