Liam Fox, the international trade secretary and a vocal Brexit campaigner during the 2016 referendum, warned colleagues planning on voting against May that her plan was the only way to be "100 percent certain" that Britain would leave.
"If we were not to vote for that, I'm not sure I would give it much more than 50-50," he told The Sunday Times.
May's government is trying to persuade a sceptical British parliament to endorse a broad withdrawal deal she struck with European leaders last month.
But the bill's passage is far from certain, with May having to pull an initial vote with a crushing defeat looking, rescheduling it for the week beginning January 14.
Pro-Brexit supporters are particularly concerned about the deal's so-called "backstop" provision, which could keep Britain locked in a customs union with the EU in order to avoid a "hard" border between British province Northern Ireland and the Republic of Ireland.
But Fox urged his colleagues to "put their own pride behind them" and take what was on offer.
"The worst possible outcome of this process would be no Brexit," he told the paper.
"For me that would induce a sense that we had betrayed the people that voted in the referendum.
"What you can be sure of is that if we vote for the prime minister's deal then its 100 percent certain that we will leave on March 29."
He also warned parliament against trying to thwart the process through a series of legislative procedures.
"Shattering that bond of trust between parliament and the people, I think, would be incendiary," he said.