Michael Madsen did not receive an Oscar nomination for portraying Budd in Kill Bill Vol. 2.
Michael Madsen is not the greatest of actors since he's given some truly terrible performances in his career. The thing is though he happens to be one actor who cannot phone in a performance, if he tries to phone it in he might as well be in comatose by how lifeless he becomes. Thankfully though when he's in a Quentin Tarantino film he seems to decide to actually try. This is certainly the case here as he portrays the Budd the third person on the Bride's (Uma Thurman) kill list due to the fact that he was part of the assassin squad who massacred her wedding rehearsal. Budd in addition to that is also the brother of the leader of the assassin squad Bill (David Carradine). Where two of the assassins carried on their evil ways, another changed but seemed more upset at being called on her crime rather than committing it, Budd is far from his days of being an assassin, now living in a trailer in the desert, and in addition reacts quite differently than the rest in regards to the Bride's quest.
This can all be seen in Madsen's only scene in which he shares with Carradine as Bill tries to warn Budd about the Bride. Madsen is terrific in the way he interacts with Carradine in the scene. There is a certain ease that Madsen brings and alludes well to the fact that they are brothers. There's an underlying warmth between the two as they speak about the Bride's previous exploits. Madsen though is effective in bringing along with this a certain passive aggressive element as he speaks to Bill, and comes off as very realistically how one brother shows his discontent with another. He is equally effective in alluding to whatever tension that was caused by something in the past, quite possibly something to do with the chapel massacre. It is not overly open about but Madsen just suggests the right disregard for his brother's advice. Both actors do very well in quickly establishing the relationship between the two brothers, despite only having this one scene together.
Madsen's best moment of his opening scene though is where Bill insists that the bride will kill him if he does not accept his help, and Madsen's delivery of Budd's reaction is flawless. Madsen particularly carries himself with a Sergio Leone style in some ways particularly when Budd remarks that they do indeed deserve to die. Madsen is exceptional as he shows Budd's living through his own regrets involving the incident in his short speech and we see that Budd has an honest remorse for his actions. What is most remarkable is in an instance where Madsen cuts down the dramatics though and finishes his statement with a silly rhyme saying "But then again so does she so I guess we'll just see won't we". Madsen does not play as though Budd did not mean his first statement, rather that Budd's simply ready to see how the chips are going to fall, and he simply does not have the right to really complain either way. It's a brilliantly handled moment by Madsen and wonderfully shows Budd's particular state of mind.
After that we briefly follow Budd through his sad state of existence in lowly job where he is treated none too well. There is technically a slight comic edge about these scenes as a former assassin has to just has to be chewed out by his crude boss. Madsen makes the beaten down state of Budd so simple, but so honest though that it's hard not to feel sorry for the guy. Despite Budd's predicament he is the only one of the assassins to actually manage to defeat the Bride in the battle as he manages to surprise her. Madsen is terrific in the scene as he shows Budd almost slightly surprised himself at the turn of events. Madsen does not portray Budd as being overly sadistic or anything like that but rather is quite great at showing Budd to be mainly happy at getting the upper hand. Madsen boisterous in the right way in the scene. His attitude is not that of a pompous jerk but rather guy who's has so few things going his way that he's just has to enjoy this moment for all its worth.
Madsen is veryy good here by making Budd far more than simply a name to be checked off the list, even though technically speaking he's one of villains. He even technically does a particularly villainous thing when he buries the bride, but even in that instance Madsen plays it as though Budd is taking no pleasure in it. In fact there again is a regret in Madsen's expression that suggests that Budd doesn't exactly want to it but rather feels that he must. Madsen always brings a great complexity to Budd in each of his scenes, and never makes him a simple evil thug. Madsen makes Budd stand out by bringing such heart to his performance so that when he exits the film I felt sadness opposed to anything else. Actually if he had been felled by the Bride instead of who he meets his end with I might have lost my investment with the Bride. This is because Madsen manages to create such an affecting portrait of a former assassin with a conscience.