So, to understand the speech, I suppose one must understand the background of it. Carter's pollster Pat Caddell told him that in the wake of not just the energy crisis, but the aftermath of the political assassinations of the 60s, Vietnam, and Watergate, Americans faced a crisis of confidence and that Carter needed to address this. Carter's other advisors tried to steer him away from Caddell's idea, and to focus more on inflation and the energy crisis, but Carter supported Caddell's theory, so the speech went ahead. It was met with resounding approval and Carter's popularity jumped 11 points, no small feat. The White House was inundated with positive calls and letters. So, what went wrong and why do we now remember it so negatively?

The primary reason is because Jimmy Carter, whatever his strengths and weaknesses, tended to make poor political decisions. In the aftermath of the speech, Carter fired several cabinet members, and generally seemed to flounder such as when Congress (which his own party controlled), rescinded, over his veto, the surcharge on imported oil and rejected his Energy Mobilization Board idea, which was to facilitate the construction of new power plants... Also, the economy never really improved. In order to combat inflation, Federal Reserve Chairman Paul Volcker instituted a very tight monetary policy, which started to reduce inflation, but slowed economic growth to a crawl. Carter enacted a program of austerity as well. This caused unemployment to rise while inflation stubbornly remained high. This coincided with Carter's re-election campaign and the country didn't begin to recover until March 1981. The feelings on the speech turned when Ronald Reagan was nominated and presented a sunny, optimistic image of America's future. The malaise speech was a critical challenge to Americans' way of life and while most Americans responded to it positively initially, when presented with the contrast of Reagan's affable embrace of everything the speech was decrying, it seems like most Americans decided that they liked that better.

As for who coined the name of the speech, it actually came from Clark Clifford, who mentioned in an offhand comment to reporters that Carter was "worried about the growing malaise in the country" and that he intended to tackle it. The name ended up sticking.

Most of this information comes out of The Presidency of James Earl Carter, Jr. by Burton and Scott Kaufman.