It would be the National Aeronautics and Space Administration.
Breaking down this sentence,
In the 1970s would be a prepositional phrase modifying, err, granted(I think)
Congress would be the subject because that's who's doing the "main" action, I guess.
Granted would be the verb, because it's what the subject is doing. And it's a verb.
Funds would be the direct object because Congress granted funds, it received the action, granted.
For a new spacecraft would be a prepositional phrase modifying... um... funds... i think.
And by the process of elimination we know what the indirect object is.
(It's the National Aeronautics and Space Administration.)
The reason why is because it's who's receiving the funds, it's who the action was performed for.
wow i need to refresh grammar.