James Buchanan was a lifelong bachelor (there are rumors that he may have been our first gay President) and didn’t have a First Lady and Grover Cleveland entered the White House as a bachelor — he was married a year after he took office. There have also been Presidents who didn’t have First Ladies because they were widowers whose wives died before they entered the White House: Thomas Jefferson, Andrew Jackson, Martin Van Buren, and Chester Arthur.
Your question about why voters place such an emphasis on having a traditional nuclear family in the White House is a good one. I would assume that part of the reason is that Americans are somewhat addicted to tradition, despite the fact that most American families that I know or have met aren’t “traditional”. I don’t think that there is such a thing anymore as an “average American family”. We are far too diverse in so many categories to call anything average anymore — and I personally believe that’s a good thing.
Another reason is that, politically, image is everything and the image of a husband, wife, two kids, and a dog promotes stability. We don’t elect playboys and we’ve only elected one President who had been divorced (Mr. Conservative himself — Ronald Reagan). The political reality is that the television sitcom family gives voters comfort, so a photogenic, happy family is an asset in campaigns — if you don’t believe that, think about how many candidates use photos of their family in their campaign ads. I don’t think it represents what American families are, necessarily, but it probably is designed to represent what image-makers think American families all wish to be.