Two cabinet ministers have announced they will resign if Boris Johnson wins the Conservative leadership race.
Over the weekend, Chancellor Philip Hammond and Justice Secretary David Gauke both revealed their intentions.
Mr Hammond, who has been in Number 11 for three years has been a vocal critic of a no-deal Brexit, something Mr Johnson supports.
"I'm sure I'm not going to be sacked because I'm going to resign before we get to that point," he said.
"Assuming that Boris Johnson becomes the next Prime Minister, I understand that his conditions for serving in his government would include accepting a no deal exit on October 31, and it's not something that I could ever sign up to."
And Mr Gauke said he was not prepared to condone a no-deal Brexit.
"If the test of loyalty to stay in the cabinet is a commitment to support no deal on October 31 - which, to be fair to him, Boris has consistently said - then that's not something I'm prepared to sign up to.
"I recognise that this spell in government is coming to an end. Given that I've been in the cabinet since Theresa May came to power, I think the appropriate thing is for me to resign to her."
The postal ballot among Conservative Party members will close at 5pm today, with the result due to be announced tomorrow morning.
Mrs May will officially resign after taking Prime Minister's Questions in the House of Commons on Wednesday afternoon.
The new Tory leader will enter Number 10 soon after.