What two major U.S. auto manufacturers went out of buisness or were taken over between 1945-1970?

This depends to some extent on what you mean by a "major"
US auto manufacturer.  There were more than two US auto manufacturers that went out of
business or merged during this time, so it is not clear which two you will want to
mention.

I would say that the two most famous auto
manufacturers to merge or go out of business were Packard and Studebaker.  These two
companies merged in 1954.  By 1958, Packard had stopped producing any cars.  Studebaker
made its last car five years later, in 1963.

These were two
of the more famous auto makers in the pre-war period.  Both had been in existence since
the earliest days of the 1900s and had produced many famous cars.  The demise of these
firms was a major example of the consolidation of the auto industry after
WWII.