Edmond O'Brien did not receive an Oscar nomination for portraying Hank Fallon/Vic Pardo in White Heat.
In this film O'Brien comes close to being lead again as the undercover agent who is put in prison to infiltrate Cody's gang to put a stop to both Jarrett, and his method of smuggling out his crime earnings. The agent Hank Fallon pretends to Vic Pardo who goes about trying to be Cody's best friend in every way so he can join the gang himself. Honestly O'Brien would be the lead in most films, but Cody is the one who always takes precedence within the scheme of things in the film leaving Hank as an observer who only acts when necessary to ensure that Cody is taken down. This leaves Edmond O'Brien to play this role rather close to his chest, and act really in the background while Cagney takes the spotlight.
O'Brien portrays the only character we can possibly sympathize with in the film as everyone else are low criminals who are either insane like Cody, or backstabbers like Cody's men and his wife. Of course O'Brien does not play Hank like the character we need to sympathize with though would works well for the rough nature of the film. Importantly above all he portrays Hank as man who is firm in doing his job and living to the end of it. O'Brien shows Hank playing the field well in the scenes where he is among only criminals and must try to embed himself within Cody's good graces.
O'Brien handles the back forth nature of the effectively going from the supportive Vic Pardo who seems to always be looking out for Cody, and supporting as the best sort of right hand man. O'Brien puts it on thickly but not too thickly as the false Vic who inserts himself with Cody by just seeming to be his biggest fan. O'Brien combines this well though through his moments which are silent reactions that show the more honest thoughts of Hank. These reactions are all very well placed by O'Brien whether it reflects his concern that he will be found out, or his sympathy for a man Cody brutally murder. O'Brien brings the appropriate realism to the proceedings with just these small moments that add to the film nicely.
This obviously is not the standout performance of the film. That undeniably is James Cagney, but Edmond O'Brien knows what is required of him in this part and goes with that. He handles his role just as it should be as basically the sanity within the insanity and to a certain degree he acts as a bit of a balancing act to Cagney's portrayal of Jarrett. He tries to be the more humane face in all the carnage and succeeds in doing so, well being the proper adversary in his depiction of Hank's ruse. Cagney is the one you remember at the end of the film but O'Brien in his solid portrayal supports the film in a very much needed fashion.