Just a hypothetical scenario
Well, first you need to know who to influence for any particular decision point. In order to maximize your influence across multiple political cycles, you need to control not the politicians alone but also a substantial fraction of the civil servants, and it's a bonus if you can get information on people with security clearances. You need to obtain the list of federal employees, what they work on, what their clearance is. So, you hack the database of the Office of Personnel Management and that gets you the list of people to influence, and whatever information came up in their security investigations.
Next you need to acquire dirt on these people. So you hack the Ashley Madison affair-dating site and see who shows up on both lists. Anyone who does is probably blackmailable. Anyone who wasn't on both lists before that you really wanted to target can suddenly be on both lists when you release the AM data publicly. Maybe you remove the people willing to play ball from the AM data first. Maybe you salt the AM data with some fake data as misdirection.
It's all circumstantial, of course. But you see what I'm getting at.
I'll probably never know if I'm right, but I see a potential connection here.
That said... anyone willing to give a credit card number to an adultery site is stupid enough to deserve the results.