U2 became very well-known on the college circuit in 1983 with the War album (and in particular New Years Day). In 1984-5, U2 were extremely disappointed that "Pride", a very catchy single and a great rock anthem besides, didn't do much better in the American charts.
The Live Aid performance is probably what really helped the mainstream public notice U2, and the live version of Bad (Wide Awake in America) was specifically intended to prepare to "break" U2 in the States (note the title!). Which it did - U2's next single, With Or Without You (with the incredibly strong Joshua Tree album of course), went to #1 and launched them into the mainstream stratosphere - the Time magazine cover and all kinds of mass media coverage and hype followed.
It was an incredible time - U2 was that up-and-coming band that had finally arrived - this was before the later anti-U2 backlashes had occurred and the feeling was really special - it just seemed like absolutely EVERYONE wished them well. Because U2's political "agenda" at the time corresponded well with that of the U.S. power structure (U2 drew attention to the many negative aspects of Soviet policy, in particular) and the band really made an effort to "woo" the U.S. in interviews, they became bigtime media darlings in the U.S. The media were only too happy to promote U2 a great rock band "with a conscience".
During the late 1987 fall leg concerts, Bono was openly and vociferously criticizing the U.S. bombing of Nicaragua - once this was recognized, the U.S. media turned very sour and the seeds of backlash were sewn. All of a sudden that "conscience" was reviled - during late 1987-1988, everyone was talking about how arrogant U2 were, their concerts were "preachy", etc. (To be fair, it didn't help that Bono probably was reading his own reviews a bit too much; and the movie Rattle & Hum did reveal quite a bit of hubris)