Theresa May has angered Tories by holding talks with Labour, with Brexiteers including Boris Johnson concerned she will accept a customs union as the price for a deal with Jeremy Corbyn.
The prime minister has told European Union leaders she wants a delay to Brexit until June 30 at the latest, with the possibility of an early exit if she can get a deal through parliament.
But Brussels is expected to demand a clear strategy from the prime minister at a meeting of EU leaders on Wednesday and could insist on a longer delay which would require the UK to participate in European elections.
In a video message recorded in her Chequers country retreat, Mrs May said both sides will have to compromise in the cross-party talks with Labour.
The negotiations stalled after Labour said the prime minister had refused to set out any changes to her Brexit red lines and no further face-to-face meetings have yet been confirmed.
The prime minister acknowledged that she could not see the Commons accepting her deal in its current form and MPs would not agree to a no-deal exit - currently the default position at 11pm on Friday unless an extension is granted.
That was the reason for the "new approach" of cross-party talks with Labour as "the choice that lies ahead of us is either leaving the EU with a deal or not leaving at all".
She said: "It'll mean compromise on both sides but I believe that delivering Brexit is the most important thing for us."
If no deal can be reached with Labour, Mrs May has committed to putting a series of Brexit options to the Commons and being bound by the result.
But former foreign secretary Mr Johnson used his Daily Telegraph column to warn that Tory MPs would not allow Mrs May to "surrender" to Mr Corbyn.
"If the UK were to commit to remaining in the customs union, it would make a total and utter nonsense of the referendum result," he said.
"To agree to be non-voting members of the EU, under the surrender proposed by Jeremy Corbyn - it cannot, must not and will not happen."