The DUP's Ian Paisley said he would like to see a no-deal option left on the table, telling BBC Two's Newsnight: "If you vote to remove this from the Prime Minister's arsenal essentially she will have to blink again".
We know that the majority of MPs don't want a no deal, but in voting against May's deal they have made that much more likely.
The stinging 149-vote defeat stripped away May's control over the course of Brexit and handed it to Parliament, which is divided about what to do next.
The office said: "With just 17 days to go until Brexit, we will continue with our European partners to prepare for a no-deal British exit in order to be ready on March 29".
This is seen (in a monstrous mix of cliches) as the "Get out of Jail Free Card" which can "get the (Tory) band back together again", in the next big set of Brexit votes later today, on the option of leaving the European Union without a deal. Notably, although some among the EU27 are rumoured to prefer a longer extension, MPs can not rely on them to impose further delay if the Prime Minister gains a specific parliamentary mandate for something time-limited.
But the fact Cox has not changed a key part of his advice on the risks of the United Kingdom being unable to leave the backstop throws into doubt whether many Brexiteers will be willing to support the deal.
"Medium term, technical structures remain constructive", says Robin Wilkin, an analyst with Lloyds Bank, but he warns, "intra-day volatility remains high".
Parliament's failure to back the divorce terms could unleash economic chaos: it raises the risk of Britain severing ties with its biggest trade partner on March 29 without a deal after 46 years of European Union membership.
He advises the prime minister to seek "partnership deals" within Parliament that might lead to a solution of the Brexit impasse.
May flew to Strasbourg, France, late Monday for talks with European Commission President Jean-Claude Juncker.
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But her hopes were dashed when Attorney General Geoffrey Cox said the changes "reduce the risk" Britain could be trapped inside European Union regulations - but do not eliminate it. An allied party from Northern Ireland and pro-Brexiteers from within May's own Conservative Party had both signaled they would not support her.
Nigel Farage MEP, who was ad hoc leader of the Brexit campaign for many a long year before the term was even coined, declared that the deal's rejection and Mrs May's subsequent decision to put "No Deal" - now the legal default come March 29th - to a free vote, with her Remainer-dominated Government having no fixed position on the issue, was a "total failure of leadership".
"Now is the time to come together to back this improved Brexit deal and to deliver on the instructions of the British people".
Brexit minister Stephen Barclay said no-deal remained preferable to staying in the EU.
The EU27 will expect a credible justification for a possible extension and its duration.
British MPs are now likely to vote on requesting a delay to Britain's departure - something that would have to be approved by the EU's other 27 member states. "If we don't check out tonight, we may never leave", tweeted Conservative legislator Bob Seely.
It has also increased the chances that May's fragile government could fall, sparking a snap election.
An opposition Labour Party spokesman said this meant she had "given up any pretence of leading the country".
Many MPs believe that the Brexit deadlock will not be resolved without a further referendum, and pursuing this outcome is now official Labour Party policy.
It also said it would not introduce new checks or controls on goods moving from the Irish Republic to Northern Ireland, a major concern among Irish politicians who feared a hard border could see a return of violence which blighted the British province for more than 30 years until a 1998 peace accord.
The Daily Express describes it as a "fresh shattering blow" for the PM that leaves Brexit "almost certain" to be postponed past March 29.