"We don't know if she is going to remain prime minister, if we are going to get somebody else, who that other person is going to be - it is a mess", Thornberry said.
Lewis, the Conservative Party chairman, said all options were on the table but that a customs union with the EU - an idea backed by the opposition Labour Party and some Conservatives - would be hard.
The rejection leaves big questions about Britain's next move on the day the country was supposed to cancel its European Union membership. Get our country back and deliver what we promised.
MPs are due to vote on one part of Theresa May's deal today, although it is uncertain whether the motion will pass.
Thousands of Brexit supporters, who had planned to be celebrating Friday, were protesting instead.
At least six senior pro-European British ministers on both sides of UK's Brexit impasse could resign, depending on what course Prime Minister Theresa May supports next week, The Sunday Times newspaper reported. Yesterday it applied to the Electoral Commission to become a political party, Change UK-The Independent Group, in time for participation in possible European elections and a possible UK general election.
Her aim is to avoid having to prosecute a soft Brexit plan that she doesn't support and which could split her Conservative Party.
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The speaker will reportedly select from the most popular options from last week so that MPs can whittle these down to a single policy, which would likely be for a Brexit based on retaining access to a form of customs union with the EU.
The British pound, which has been buoyed in recent weeks by hopes that the likelihood of an abrupt "no-deal" Brexit is receding, fell half a percent after May lost, to as low as$1.2977, but then recovered some of its losses.
"My position is that it is not the responsible thing for a government to do, to leave without a deal in these circumstances, so obviously I wouldn't be able to remain a member of the government that pursued that as a policy".
He said staying in a customs union with the EU would go against the result of the referendum and the Conservatives' election manifesto.
Some protesters dragged dummies wearing masks of May and Labour Party leader Jeremy Corbyn through the streets, leaving them outside the gates to May's Downing Street residence.
MPs have repeatedly rejected a "no-deal" outcome, fearing catastrophe if Britain severs ties with its closest trading partner with no plan in place.
One placard said: "Politicians worth their weight in cow dung". "Today we can show that we can come together in the national interest".
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Under existing arrangements, London now has until April 12 to either present an alternative Brexit plan or leave the European Union without a deal.
But EU officials have suggested they may agree to a lengthy delay to Britain's departure if United Kingdom politicians agree on a plan.
"There are those who will say: 'The House has rejected every option so far, you'll probably lose so why bother?' I bother because this is the last opportunity to guarantee Brexit", May told the House of Commons.
"Her deal is no more", he said.
A Brexit supporter wears the Union Jack colors on his face at Parliament Square in Westminster, London, Friday, March 29, 2019.
May now three options: go back on her word and lead the country out of the bloc without a deal on April 12; ask the European Union for a long extension to rewrite her whole Brexit strategy; or call a general election as a way out of the impasse.
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