How would she have gotten a baby into the country? Even in 1961 you had to have a baby added to your passport in order to travel with them. A woman attempting to bring a baby into the United States, that was not included on her passport would not have been allowed into the country without first getting documentation for the baby.
Well, since we haven't seen any records, how do we know that she didn't?
But if BHO Jr was actually born in Canada, then zipping accross the border in a private auto would have been easy. Several folks who lived near the border in those days report that they only checked the "papers" of the driver (and that would have been just a driver's license). August 1961 was well before 9-11-01, and even somewhat before folks started hijacking airliners to Cuba.