Well, except for the stints in rehab and propensity to marry gay men, Gloria was in a very similar place at the same point in her career. Gloria was also desperate for a comeback, er, "Return" before Sunset came along, having been virtually forgotten by the film industry for nearly two decades (about the same amount of time since Liza's last successful film -- Arthur, wasn't it?).
There aren't a lot of great film roles out there for Liza, but the crazy, over-the-top, larger-than-life Norma would be right up her alley. I think she could easily capture Norma's delusional mindset, haughty yet vulnerable demeanor and, even in her present vocal state, could sing the score at least as well as Glenn Close. There's also something very "old Hollywood" about her (in part, because of her parents and in part because of her own career which has always been very "old school") that few other actresses today could convey. I doubt that any studio would cast her, but in many ways she'd be ideal for the part.
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
[http://margochanning.broadwayworld.com/]
"The Devil Be Hittin' Me" -- Whitney