In November 1943, a NORC survey asked "If you had a son just getting out of school, would you like to see him go into politics as a life work?" This question has been repeated in a number of surveys since then, most recently in 2015 (sometimes with minor variations in wording).* Confidence in government and political leaders has declined over that time, so you might expect a decline in the number who want their hypothetical son to go into politics. However:
it seems to have increased--it definitely hasn't declined. (I show the ratio of yes to no answers because the proportion of "don't knows" has tended to decline). The highest single value was in March 1965 (36% yes and 54% no), when Lyndon Johnson had won a landslide victory and had a 70% approval rating, but March 2010 was almost as high (36% yes and 55% no), although Barack Obama's approval rating had fallen to about 50% and the Tea Party movement was getting underway.
Why did interest in having a hypothetical child go into politics increase when approval of politics and politicians was declining? One possibility is increased educational levels--more educated people may be more likely to think that someone like them could accomplish something in politics. Another is that growing ideological distance between the parties and increased focus on national rather than local politics has given people a sense that more is at stake--that politics is potentially about accomplishing important things or stopping harmful things, not just dealing with routine everyday affairs.
I hope to come back to this--I have a feeling that there is something important here.
*More recent surveys usually ask about "son or daughter." Some have asked randomly selected halves of the sample about a son or a daughter--there is little or no difference in responses.