Reformers started fighting corruption in government back in the 19th century after most city and state governments had been taken over by political machines. The machines usually owned the congressmen and Senators as well.
The reformers came from both parties, because in various cities either the Democrats or the Republicans were the ones with the power. The reformers took over the other party to fight them. Some of the third party movements, especially the Progressive Party, had platforms that included anti-machine planks. The referendum, the initiative, recall, city manager (i.e. non-partisan professional instead of mayoral) government, all came out of these movements.
There was also a move to the secret ballot. With open ballots the machines knew who everybody voted for, so they could reward or retaliate against votes. The secret ballot prevented this, for the most part. (It’s also true that voting percentages were down with secret ballots because there was no way to get the easy reward. Some historians argue that this was done deliberately to get the lower classes that supported the machines to stop voting.)
Although the reformers gains were always short-lived - they got the really corrupt crooks out or in jail but didn’t give the masses a good reason to continue voting for them - they forced the worst abuses to stop and made the politicians more sophisticated in their graft.
What truly killed the machines, though, was the death of the city in the 1950s. When the suburban population grew larger than the city population it became impossible for the machine to maintain control.
Politics went wholesale instead of retail, meaning that you had to attract the support of dispersed masses through advertising rather than personal contact. This also made it easier for outsiders to challenge for control. Individual outsiders can be crooked, as we’ve seen again and again, but the kind of institutional crime that the machines did routinely is far harder today than it used to be.
The mainstream media has helped this despite the canards thrown at it. Newspapers used to be totally partisan and controlled by or in bed with the machines. Gradually the neutral style pioneered by the New York Times and the growing professionalism of the journalist meant that newspapers were harder to bring in line and more likely to expose what politicians were doing, who was giving them money, and whether their votes or influence was being bought. Despite the bleating of certain bloggers this was and is a good thing. More scrutiny means that politicians have to be crazy to try to get away with anything. Again, many individual politicians are crazy and so they do try. But they get caught and their careers immediately end.
When people say that politics today is basically more honest and open today than it’s ever been, believe them. No average voter today could imagine or stomach the level of corruption that was standard in almost every city, town, village, county, or statehouse in the country, not to mention Congress, a mere 100 years ago.