Dallas was the highest rated TV episode ever at the time, with an estimated 83,000,000 people watching.
The cliff hanger was such a phenomenon that J.R. items were everywhere, like shirts, posters, JR Beer, and of course, buttons like this from the Busy Beaver Button Museum, were produced in high quantities. According to Wikipedia,
During the presidential campaign of 1980 (which led to the election of Ronald Reagan), the Republicans edited an official badge saying, “A Democrat shot J.R.” which influenced the polls according to some sources.
Jimmy Carter claimed that he would have had no problem financing his campaign if he had known who shot J.R.