Dame Caroline Spelman, a Christian, also expressed regret that some Tory Brexiteers and the Democratic Unionists had so far refused to support Mrs May's deal.
The representative for Meriden in the West Midlands said: "To get the deal through Parliament, I think nobody deserves that more than Theresa May (pictured leaving Parliament on Wednesday evening).
"That would be her legacy and I think that she would feel she achieved what she, partly, set out to do."
If Parliament passes the Withdrawal Agreement before 11pm on Friday, the UK will qualify for a Brexit delay - until 22nd May - agreed by the European Council last week.
Dame Caroline said she had suspected during Wednesday's Prime Minister's Questions that Mrs May might have already decided to promise to quit as PM if her deal is approved.
The politician added: "She's not somebody who sought high office - it was thrust upon her. The situation was not created by her - and she's trying to resolve it.
"There were lots of kind things said about Mrs May yesterday [during a meeting of backbenchers where Theresa May made her announcement] but I shall be sorry to see her go."
Click here to listen to Premier's Alex Williams speaking with Dame Caroline Spelman:
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