How problematic is it to put a 26X1.75 tire on a 38mm rim?

I have Bontrager 26" X 38mm rims on my bike, and am interested in putting Town & Country 26X1.75" tires on it for the summer (don't ask). Sheldon Brown recommends tires be at least 1.45 times wider than the rims, and this will not be. Will this cause any problems due to the tire being too narrow? If so, how likely are these problems, and how serious are the problems to be, if they are likely to happen?