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.