I've never seen polling to this effect. The best I've been able to find was a pew poll from early last year which stated 58% of government regulation does not go far enough WRT AI. The lack of useful specificity on what they mean by common sense is concerning. People should know what they are supporting beyond nebulous slogans especially in this space.
If AI ever really starts getting real it won't just be AI companies pushing for regulation to protect their own market share it will be industry generally to protect corporate interests from erosion by those who might leverage the technology to disrupt and displace them.
The billion dollar global scare mongering AI lobbying blitz after all was pushing FOR regulation not against it. What the AI companies are angry about is not a lack of regulation but regulation that cuts against their interests and patchwork regulation in which every state has their own disjointed set of rules.
The most immediate salient public threat from AI is those with power viewing AI as a source of more power. Insane money pouring into AI isn't just about misplaced investment it is driven by fever dreams of the powerful. None of what they are dreaming about has a nexus to the public good.
This is one case where details especially matter given both sides want regulation and there is no such thing as "common sense" when it comes to AI.