"It is clear that this House does not support the deal. This deal now has to change. There has to be an alternative found," opposition Labour leader Jeremy Corbyn said.
"And if the prime minister can't accept that then she must go, not at an indeterminate date in the future but now."
Tired of waiting, MPs this week gave themselves unprecedented powers to vote on a range of options for Britain's future relationship with the EU.
A proposal for a new customs union got close to passing in a first round, as did a plan for a referendum on May's deal, with more voting planned next Monday and Wednesday.
The risk that MPs decide to agree closer ties to the EU, or even stop the departure process altogether, focused the minds of some Brexit supporters, who reluctantly agreed to back May's deal.
Her offer on Wednesday to quit if it passed also helped persuade some of her staunchest critics, including former foreign minister Boris Johnson.
But 34 of the 314 Conservative MPs voted against the deal, as did the 10 MPs in May's Northern Irish allies, the Democratic Unionist Party (DUP).
The party says planned arrangements to keep open the Irish border after Brexit -- the hated "backstop" plan -- is unacceptable.
"We are not prepared to see our constitutional position altered by Brussels in a fit of pique for daring to leave the EU," said MP Sammy Wilson, the DUP's Brexit spokesman.
Snap election?
May's offer to quit fired the starting gun on an informal race for the leadership of her Conservative party.
Her resignation was dependent on getting the divorce deal passed -- and she might try one last time to get her deal through.
Even so, her days are numbered, as increasing numbers of Conservative MPs are openly talking about when, not if, she will step down.
Getting another vote on a deal would be tricky, as parliament speaker John Bercow has already warned he will not let her bring the same deal back again and again.
Under an agreement struck with EU leaders last week, Britain would have left on May 22 if MPs approved the deal this week.
Officials believe there is still a chance that, if she can get it through before April 12, this date is still possible. However, speculation is also growing that the only way out of the impasse is a snap election.
(Source: AFP)