The British pound rallied Wednesday on expectations of the sides managing to avoid a messy breakup in the coming days.
That instability increases the chance of an early British election, which could rearrange Parliament and break the deadlock.
Smith says May known as the election to strengthen her hand in delivering Brexit, but was weakened when she lost her majority.
"This is a decisive moment in the story of these islands and it requires national unity to deliver the national interests", said May.
Yvette Cooper is behind a bill which could prevent no-deal.
"It is very unlikely that there will be any crash out at the end of next week with the prime minister looking for an extension with a plan to go with that".
A hardcore eurosceptic group of Conservative has refused to back the divorce deal she struck with the European Union, saying it did not represent a decisive break with Europe.
Tory MP David Jones asked if Mrs May still thought Mr Corbyn was ‘not fit to govern
But some in the Labour Party have cast her gambit as a trap aimed at scaring her own lawmakers into backing the thrice-defeated deal, or as a way to extend responsibility for the difficulties of Brexit to the Labour Party.
But a no-deal Brexit is still the legal default position, and could happen if the European Union refuses to grant another extension. This will focus on the future relationship.
Currently, EU leaders are due to have a big meeting on 10 April (next Wednesday) at which they will discuss the UK's future.
The DUP in a statement said May's "lamentable handling" of the negotiations with the European Union had been a complete failure and it "to be seen if sub-contracting out the future of Brexit to Jeremy Corbyn, someone whom the Conservatives have demonised for four years, will end happily".
In the past two weeks, rank-and-file politicians have taken control over the Parliamentary agenda in an attempt to solve the crisis themselves.
The EU would be "open" to such proposals, but it was for London to put them forward, he said. "It now seems all too likely that British trade policy and key law-making powers will be handed over to Brussels - with no say for the United Kingdom", he added, insisting that there were no circumstances in which he could support being part of a customs union with the EU. "I don't want to set any limits, one way or the other, ahead of those meetings".
Juergen Maier urged lawmakers to maintain Britain in a customs union with the EU, saying that would enable frictionless transaction to last. "And we'll ensure that those are on the table", he said.
With Britain dashing toward a disorderly exit from the European Union within days, May pivoted away from the cliff edge on Tuesday, saying she would seek another Brexit delay and hold talks with the opposition to seek a compromise.