If the war continues at this point, it is likely that the US could make significant gains.
Its strength is real - fission bombs produced at an average of one every two weeks, deliverable
by long range heavy bombers, some of which would soon be able to reach parts of Europe if
necessary. The Unity has less bombs, produces perhaps one for every three American bombs, and
is not capable of delivering the weapons anywhere in the Americas (they would, in fact, have
problems reaching Australia). At this point, however, both sides are somewhat blinded by the
fact that the other side possesses the bomb, and are more concerned with what the enemy might
do with the bomb, than with what they could do with the bomb. The Americans, in particular, are
unaware that Unity long-range missiles cannot carry the bombs, and that the Unity has such an
inferior production rate. Both sides make what is, given their knowledge, the sensible choice -
agree to a cease fire that preserves the status quo, depriving them of no potential conquests
that would not be long and bloody even with the atomic bomb.
1956 - The Rio Accords
In our timeline South America remained something of a backwater, isolated from and often
disinterested in superpower struggles. Near the middle of the century, most of the continent
is actually under more-or-less democratic governments as in our timeline. In our world, South
America falls almost entirely to home-grown authoritarianism, and its position relative to the
rest of the world declines for decades. In the world of the Unity, it is obvious to every
remaining democratic and not-so-democratic free nation who the real enemy is, and that they are
a significant long-term threat. The Unity has just succeeded in bringing the majority of the
planet under its control by means of conquest, despite the best efforts of its victims and of
the fully-mobilized United States. The long-term potential of the Rio Accords, an agreement
which does lead primarily to the South American nations surrendering much of their independance
in key areas such as defense and trade, is to prevent the rise of authoritarianism and the
relative decline of most of South America in relation to the rest of the world. It is, however,
a two-way street with a focus on the long term - the surviving Allied Powers (the US, Canada,
and Australia) go to substantial expense investing in and developing the industries and markets
of their southern compatriots.