How important was the second earner issue when the progressive tax code was invented?
The answer: not very important. I couldn't find data back before 1960, but Pew had this graph from 1960 to 2010 (click image to go to their source page).
This suggests that back in the 1940's and 1950's when the withholding system and progressive tax brackets were thought up (EDIT: 1913 was first income tax in US, 1942 was when then invented withholding and set the bottom bracket to double-digit percentages. See Wikipedia), the fraction of households that would be affected materially by the second-earner being kept out of the workforce by high marginal tax rates was negligible. In particular I'm just going to guess and say maybe 80% of family households had only the father employed in 1950 and even those where the mother was interested in work, how many women actually had the education and qualifications to have jobs rivaling their husbands earning power, such as Lawyers, Surgeons, Engineers, Advertising Executives, or whatever it was that made you the big bucks in 1950? It couldn't have been more than on the order of 1% or so.
EDIT: This graph from Wikipedia shows only about 5% of the whole population had completed a bachelor's degree.
This link to Wikipedia shows that the "modern" tax code in which the first tax bracket was double-digit percentages started in 1942.