How close did Chamberlain come to staying PM

[rob in cal]

   Neville Chamberlain resigned as PM on May 9-10th, 1940 because in a vote of confidence, 38 Tory MP's voted against his government, and another 20 or so abstained. He still had a majority of 81 in the commons, but the big amount of defections was the main reason for his resignation.  My question is, what was the level at which he would not have resigned?