Mr McKenzie thought National voters would be in a better position to afford the 75 cents each text cost.
A TVNZ spokesperson said it had no rules against multiple voting. Its polling company could see if there were a significant number of votes from one phone but that was not common. Different members of one family may well vote using the same phone, TVNZ said.
"Our polls are not scientific and we have never promoted them as such. They are simply an indication of which way the wind is blowing, and an opportunity for people who are really motivated to interact with our programmes. The cost of each call acts as a natural deterrent to any extremes.''
Bryce Edwards, from the University of Otago's politics department, warned that polls conducted by the media were inaccurate, as they made no attempt to recreate an accurate cross-section of society.
But perceptions created by polls and the media could have a large effect on people's voting behaviour.
"If a party is seen to be doing badly, people don't want to vote for them.''
Dr Edwards said the Labour Party was especially suffering from this phenomenon, and he thought voters might be disheartened by the party's poor portrayal.