If she was so drunk for so long that she didn't even realize he was dead at the bottom of the stairs for quite some time, how would she remember that she pushed him? Is it possible that he fell down the stairs by himself since he was also drunk? Presumably, since he sat for weeks at the bottom of the stairs, no third party was there to witness the event. In the absence of evidence that she actually pushed him down the stairs, I wouldn't think there would be any legal basis for manslaughter, let alone murder.
Morally, though, I would consider that murder. She must have formed the intent to push him down the stairs, even if that intent was formed only a nanosecond before she pushed him. That he would be injured, perhaps gravely, after being pushed down the stairs is completely foreseeable.