There are multiple aspects to this. One is the development of party discipline (something that began earlier than we might assume, with the reform of House rules in the late 19th century) meaning that party members have less of a motivation to try to convince people on the other side. Another is the shift from printed media to radio and then television, meaning that Congresspeople's audience is the general electorate rather than just their house's floor. It was a gradual process, but it was already complete by the 1970s when Mayhew wrote his influential book on Congress.
It's not so much try to convince people on the other side in my opinion, but to convince other people through pointing out holes in one person's argument, or forcing him or her to defend his point of view on record.