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The lobby group is using the poll to urge the Government to adopt ACT MP John Boscawen's private member's bill to amend the "anti-smacking" law.
Just two people have been prosecuted since the controversial legislation became law in June 2007, and the second was dealt with by diversion.
Deputy Police Commissioner Rob Pope said this month the figures showed police continued to apply discretion in handling "anti-smacking" cases and Prime Minister John Key has said he would change the law if parents were prosecuted for lightly smacking their children, but so far the law appeared to be working as Parliament intended.
But Family First says the poll, which it commissioned, showed the Government should adopt a law change rather than rely on police welfare agencies' discretion.
The poll, by Curia Market Research, surveyed 1000 people.
* Extensive support for a law change across all demographics, or four out of five people.
* Three out of four said the law was not at all likely to help reduce the rate of child abuse
* Only one third of respondents actually understood the law correctly
* Forty-five percent of mums of under 12s have smacked illegally in past 12 months
* One quarter of mothers were more likely to vote for political party that commits to changing law
The poll, conducted last week, had a margin of error of 3.2 percent.
"This poll confirms that the prime minister has not reassured parents. They are still concerned that he is willing to retain a law which he admits is a 'dog's breakfast', badly drafted, extremely vague, and had to whip his MPs to support," said Family First director Bob McCoskrie.
Following last year's referendum of the law, polling showed 52 percent wanted a law change and 27 percent supported no law change but greater discretion as suggested by Mr Key, Mr McCoskrie said.
"That has now almost returned to the 80 percent benchmark of opposition to the law that has been present for the past five years.
"A law that requires so many compromises, guidelines, helplines, reviews, and parent education could be easily fixed with a simple amendment. That's what parents deserve, what they want, and what the politicians should respect and act on."