Former Education Secretary Justine Greening, who was tipped by members of the new Independent Group of MPs as being poised to quit, said that she would be unable to stay if the Conservatives became "the Brexit party."
"The question for the Conservative party is have we been consumed by Brexit?" Greening told the BBC Radio 4 Today programme.
"If we simply become the Brexit party we do not have a successful future."
She said that while she had decided not to quit "for the moment" she would not remain if the prime minister pushed Britain towards leaving the EU without a deal.
Greening was supported by the former Attorney General Dominic Grieve.
"I would certainly cease to take the whip if I thought the Government was about to take us into a No Deal Brexit. I am absolutely clear about that," Grieve told BBC's Newsnight.
"I would have to leave the party."
Former Conservative minister Philip Lee, who resigned from the government over Brexit, is also on the watchlist for a possible defection.
The warnings come as the Labour party leadership also braces itself for further walkouts from disgruntled MPs over the coming days and weeks.
Labour MPs Ian Austin, Siobhain McDonagh, Ian Murray and Margaret Hodge are all reportedly considering their positions , with others also publicly speaking out about their frustration with the party's direction under Jeremy Corbyn.
The ongoing splits come as the prime minister struggles to secure changes to her Brexit deal that will allow it to pass through the Houses of Parliament.
In a joint statement on Wednesday, May and President Juncker said they would "continue to explore the options in a positive spirit."
UK officials will again travel to Brussels on Thursday to further discuss possible legal "assurances" that can be made on the subject of the controversial Northern Ireland backstop.
However there is little sign of a breakthrough with MPs due to vote again next week on what steps the government should take.
