Mrs May told the Commons that a longer extension would require Britain to vote in European Parliament elections later this year - which she said was "not the right outcome". The cabinet is due to meet at 08:00 GMT.
The EU said no deal plans were "more important than ever" after the defeat.
Tonight's parliamentary vote sees Mr Boles join forces with MPs including Conservative MP Oliver Letwin, Labour MPs Yvette Cooper and Hilary Benn, plus Anna Soubry and Chuka Umunna of the Independent Group of MPs.
May responded: "The deal that he's proposing has been rejected several times by this house".
Mrs May said the plan was unworkable, highlighting how any transition period would require a deal with the EU.
"The deal doesn't deliver what my constituents voted for, whether they voted to leave or remain".
In the Commons on Tuesday evening, Labour Party leader Jeremy Corbyn said Mrs May should now call a general election.
But he did not mention his party's commitment to back another referendum.
Opposition MPs blamed strong-arm tactics by Tory whips as Dame Caroline tried to pull her amendment before it came to a vote.
Heidi Allen MP
"Last night's agreement with the European Commission does not contain anything approaching the changes Theresa May promised Parliament and whipped her MPs [lawmakers] to vote for", the Labour leader tweeted. "We are committed to ratifying this deal before 29 March".
Speaking in a croaky voice as husband Philip looked on from the public gallery, she urged MPs to support a "substantially better deal than eight weeks ago".
She will tell MPs whether she will vote for no deal or not when she opens Wednesday's debate.
Leading Tory Remainers and Brexiteers, including Dominic Grieve and Boris Johnson, have suggested the prime minister's deal is now "finished" and other options must be brought forward.
'In practical terms the only way no deal can be stopped is by revoking Article 50 or agreeing a deal.
Opening the session, Mrs May joked that International Development Secretary Penny Mordaunt "very helpfully offered to teach me sign language" - with her Cabinet colleague having previously used it at the despatch box.
Some of them believe it's time now to go hell-for-leather to leave without an overarching deal but move to make as much preparation as possible, and fast. "Tonight she's not even showing the leadership to whip on no deal".
Mrs May agreed but insisted her deal is a "good deal" and she wants the United Kingdom to leave with a good deal.
"I feel like MPs like myself who want to honour the referendum have been put in a bind".
Venezuela still in dark, Juan Guaido wants ‘state of alarm’ declared
Their presence "entails risks for the peace, integrity and stability of the country", Foreign Minister Jorge Arreaza said . Engineers have restored power in some parts of Venezuela, but it often goes out again.