Pippin said: "Three Christines come to mind: in order of preference
Ebersole
Baranski
Andreas
other options:
Bernadette
Donna McKechnie
Patti
Beth Leavel
nancy Opel
Imelda Staunton (she's my top choice for every female part in the history of musical theatre)
The first time I saw Mame with Angela Lansbury was June 25, 1966, about a month after it opened. That performance (and performances) may be the single most memorable in a long lifetime of attending musicals. I was delirious with 15 year-old happens. I am very protective of it, in a way that I am not with Hello Dolly, because I have seen a lot more good Dolly's than Mame's. It is a harder role IMO, and more essential to the entire show working.
I saw Baranski when she was in DC 5 - 8 years ago and thought she was terrible. The basic problem: she would make a great Vera and they cast her as Mame.
I love Bernadette and Patti, but they are too old for Mame. She ages 30 years over the course of the show. Also, IMO it is IMPORTANT that Mame dance -- the title number just would not be as effective if Mame wasn't out there kicking as high as the chorines (not to mention That's How Young I Feel, It's Today and Open a New Window) -- and I don't remember either one of them ever really dancing. Christine Ebersole might be a possibility -- don't know if she can dance, but its moot. None of the others have the combination of talent and star power necessary to pull it off.
I do believe a big talent with huge charisma is needed to make it work. Re Broadway talents, I can think possibly of Sutton Foster and Audra MacDonald when she gets past her current project and is ready to work 8 shows a week again. She demonstrated in Shuffle Along that she can do anything and can be a big box office attraction in the right vehicle. I'll throw one more Broadway veteran who is probably too old, but how about Donna Murphy? She has charisma, can do comedy, has a better voice than required, was great in Lucy and Jessie at Encores. Been away long enough that she is not going to sell a lot of tix in advance, but her reviews will help after it has opened.
Other possibilities: Jennifer Lopez has said she would like to do Broadway...I think she could pull it off. She is glamorous, does light comedy well, can dance and can sing pretty well. AND she would sell tickets. Also, how about Amy Adams? I don't know if she is interested in doing Broadway, but she was excellent in Enchanted, and is about the same age Angela Lansbury was when she was cast. I think she would sell tickets also, though she probably doesn't have the rabid fans that Lopez does.
Having seen Carmen Cusack on the road in South Pacific, and based on her recent reviews, I'll bet she would be terrific, but this probably a non-starter unless it was done at the Roundabout and didn't need a name. Finally,
Re other comments, Megan Mullally is a Vera and would probably be a very good one. Jan Maxwell IMO could not pull it off. Hell, despite the undying love a lot of people here have for her, she couldn't get through Lucy and Jessie without practically falling on her face. Toni Collette sounds interesting...maybe this could make her a star the way the original did with Lansbury. She was a name before, but not a star. I am not a huge Krakowski fan, but she can do comedy, she can dance, and a lot of people feel she has enormous charisma, so it would be interesting...although, to adapt someone else's suggestion, maybe a Krakowski led production would need to be via Roundabout. (Plus, she might be a better Vera).