There have been surveys on that. I think somewhere around 25-35% of the people who are asked if a person born in Canada to US parents is eligible, say no. They might vote for him anyway, since eligibility is not required to hold the office.
I don't know if that comports with your sense of "very few." Just saying, I'm not disagreeing with you. I'd vote for a naturalized citizen for the office, myself, if they were strong on the borders and strong on personal independence, RKBA, etc. I might even vote for a foreigner for the office, Netanyahu would be great, Thatcher was awesome.
Very good points.