This is what I would do, and what I've seen work on these boards:
Wife: "I don't want a divorce; I want to work on our marriage!"
You: "Oh?"
Wife: "Yes."
You: "What changed?"
(let her explain her thinking)
You: "That's very different from what you were saying and doing just a few days ago. I'm not sure how I feel about that, or about this marriage anymore. What's different? What changed?"
(let her explain again) Do NOT go all "melty man" at this crucial point (hat-tip to PDT here)
Then I would say "I need to think about all of this. I'm not sure how I feel about it anymore. Let's talk more this weekend, maybe on Sunday."
And then RE-DETACH.
Trust me . . . IF she is sincere . . . she will come to you, repeatedly. YOU WILL KNOW. Do NOT make this too easy on her. "This is your mess; you need to clean it up" should be your position.