What quote by Norman M. Thomas made him famous in 1944?
First of all, Norman Thomas was not particularly famous in 1944. He did run for President 6 times between 1928 and 1948. However, he did so as candidate of the Socialist Party and so was not particularly well-known.
Thomas is now somewhat famous among conservatives for a speech he allegedly gave in 1944. He is supposed to have said that socialists could get everything they wanted by just calling themselves liberals. He said that Americans would swallow all of the socialist program without knowing it. This story appeals to conservatives who believe that this is what is happening today -- that Pres. Obama is making the country into a socialist state.
The exact quote attributed to Thomas is in the snopes.com link. The quote, however, is probably not accurate. It was first used by Ronald Reagan in the 1960s, but there is no record of the speech and one of Reagan's main biographers has been unable to find where Thomas said this.