In all likelyhood Mr. Ford would have found alternate funding. But...you never know and niether shall we. During WWII, time differences would have been more critical IMHO. Hitler didn`t think things through and made decisions on a whim because of certain conditions. Troops were in Vietnam by the end of the 50`s and the war was "publicised" in the early 60`s and brought "home". Kennedy simply increased the troop counts. During this time, great instabilities were occuring and soviet intervention would have been likely. The "bay of pigs" incedent was a very unnerving time in world history as it was as close to Nuclear war as we have yet to come.
Therefore, delaying the "manhattan" project could have something to consider.
With hindsight, we think we have the knowledge to make a change but I feel sure that we would make another equally dangerous alternative time line.
So...when someone walks up to you with a time machine capable of what we have discussed, destroy it without provocation and aforethought. Man needn`t mess with time, we can make a fine mess without this type of power.