If Parliament rules out no deal, MPs will be given the option of a "short extension not beyond the end of June", Mrs May told the House of Commons today.
But Brexiteers in her own party mounted a show of strength in votes on Wednesday night, with over 100 Tory MPs breaking a three-line whip to oppose the move.
Legal experts have advised the German parliament that any Brexit delay beyond the European elections on 23-26 May could be in breach of EU law and leave the United Kingdom open to legal action, according to a confidential report seen by Die Welt.
Any delay would have to be approved by the 27 other European Union nations, Michel Barnier told France Info radio.
But some questioned what it would achieve without a breakthrough in London, where MPs still can not agree how to implement the 2016 Brexit referendum result.
French President Emmanuel Macron, speaking in a joint news conference with German Chancellor Angela Merkel, said a Brexit delay would need to be "justified" by "new British choices", suggesting that May's Government would need to signal where this is all headed - versus asking for more time just because they are stuck. "That's what will determine the length of any extension", Barnier said.
This follows the tumultuous events in Westminster yesterday when MPs voted on amendments to the Brexit deal.
Her U-turn on Tuesday prompted outrage among hardliners in the ruling Conservative party, with influential anti-EU MP Jacob Rees-Mogg warning that "any delay to Brexit is a plot to stop Brexit".
Dominic Raab said it was time for Britain to "stand up" to the European Union, as he warned a delay to the UK's withdrawal would reduce the chance of securing a deal.
The European Court of Justice, would ultimately decide on whether non-participation of Britain in the European elections is legally permissible.
Yes. They are known as amendments and, if approved by a vote, could exert political pressure on May to change the course of Brexit.
MPs also voted on several other amendments from backbenchers, including approving without a vote Conservative Alberto Costa's stipulation that May must seek a treaty on citizens' rights after Brexit under any scenario.
But the government announced a deal with Eurotunnel to "deliver improvements which will ensure the Channel Tunnel is ready to continue to keep passengers and freight moving post-Brexit" such as better security and traffic flow at the border.
It will take a legal Houdini to conjure up language that convinces Parliament that Britain can walk away from the customs union, the EU that the integrity of the single market is protected, and Ireland that there will be no customs infrastructure at border.
Lawmakers rejected a bid Wednesday by the main opposition Labour Party to force the government to embrace its alternative Brexit plan, which calls for retaining close ties with the EU.