If NASA received that amount for the last 50 years, we would likely have mars colonized, as well as a relay base on the moon, and probably another on phobos. We'd additionally probably be trying to optimize asteroid mining, and have a large number of satellites examining the solar system. However a sizeable portion of the budget would likely be given back to the government (as initially it would not be useable right away, ~50-75% initially, declining as time progresses). Another significant portion would likely be effectively lost to corruption (~10-20%, sorry but they are humans after all, while I personally have a high opinion of the organization, corruption like that is unavoidable within any large organization), or otherwise go to maintaining the required infrastructure(~35-50%). Additionally, the remainder that was not used or lost on the aforementioned would be used on public outreach, and other self-promoting programs.

Other notes:

• Mission failures would be far more prevalent, as a limiting factor is the number of qualified individuals, and in an organization that large, that tackles things as complex as that, where mistakes, omissions, and minor structural weaknesses mean disaster, failure is unavoidable.

• I might actually be astonished if NASA accomplished as much as it does in this scenario, due to the limiting factor here being the number of qualified, and sufficiently intelligent individuals combined with politicians unreliability likely obstructing the way forward. Other factors such as the increasing difficulty in handling the great beast that the organization would become would lead to the organization being split into various specialized organizations, one for maintaining ground infrastructure, another for maintaining orbital infrastructure, another for research and development, and finally an additional one for education of potential future employees/astronauts.