Data from standardized testing suggests the average U.S. president has an IQ around 130. Since most of the data is quite old (since the presidents were quite young when tested), the scores are mostly based on white norms, since there were fewer non-whites in America in past generations and because in the past it was common to exclude non-whites from the standardization of IQ tests so that an IQ of 100 would reflect the white average (of males and female combined). According to Richard Lynn, there’s about a 5 point IQ difference between the sexes that emerges after puberty and can be explained by sex differences in brain size.
An average IQ of 130 suggests U.S. presidents (who until Obama, were exclusively white) are about 27 IQ points smarter than the average white man (IQ 103). Since the IQs of marital partners correlate 0.45, I would expect the average First Lady to be 28(0.45) = 12 IQ points smarter than the average white woman (IQ 98).
Thus the average First Lady might have an IQ around 110 (12 + 98)
Although people like James Carville have gushed for years that Hillary Clinton is the smartest woman in America and has an IQ that would make water boil, there’s no evidence than any First Lady in American history had an IQ above 140.
First Ladies are interesting because they are usually the most admired woman in America on the annual Gallup poll, however both Michelle Obama and Laura Bush were overshadowed by both Oprah and Hillary Clinton. Historically, First Ladies would go away when their husband’s presidencies ended, allowing the spotlight to be on the current First Lady, but Hillary Clinton has managed to very adaptively parlay her First Lady status into a spectacular political career, thus overshadowing her successors. In this way she is very similar to George W. Bush who turned his status as the son of a president into incredible political success of his own, or like Donald Trump who turned the wealth he inherited from his father into an even larger fortune.