The leaders rejected May's request to extend the deadline until June 30.
United Kingdom media reports claimed that disgruntled Tory lawmakers, along with a section of her Cabinet and Ministry, is plotting to give her an ultimatum to resign.
Lidington would step in to deliver Brexit before a (nother) leadership contest is held in the autumn. A leadership challenge by hard-line backers of Brexit failed in December last year and she could not be challenged under party rules for another year. However, they don't appear to have settled on an interim replacement.
The Sunday papers carried lurid reports of supposed cabinet plots to replace May with a caretaker prime minister, and both her de facto deputy and the environment secretary were mentioned as being in the frame.
"We've made sure over the last two years we have very good links not just at prime minister-level and taoiseach-level, but also between Phillip Hammond and Pascal Donohoe, between Simon Coveney and David Lidington and so on", he said.
Now a departure date of May 22 will apply if parliament rallies behind the prime minister and she is able to pass her deal.
"To be talking about changing the players on the board frankly is self-indulgent at this time", Mr Hammond told Sky News's Sophy Ridge On Sunday.
But there has been growing angst about Ms.
Protesters are gathering in central London before what is expected to be a massive march in favor of a second Brexit referendum.
If she succeeds, Britain will depart on May 22 under the terms of the withdrawal agreement the prime minister struck with Brussels past year. On Sunday several Tory MPs came out against Ms.
His visit to Downing Street came after he was "bombarded with text messages" and urged to confront the Prime Minister.
He tweeted "I'm afraid it's all over for the PM". "She's done her best". You're plunging this country into chaos. Trust in democracy is collapsing. This cant go on. "We need a new PM who can reach out and build some sort of coalition for a Plan B (Brexit)".
Despite May's letter to lawmakers, it was not clear what path her minority government would take this week.
A majority of MPs voted against holding another referendum on the issue earlier this month, and it remains a longshot bid by Remainers.
MPs will vote on their favoured Brexit outcomes on Monday night against expectations a third vote on May's deal is defeated. If the deal is not passed by then, Ms.
The rift within the cabinet between May and her cabinet has erupted over the fate of the Brexit deal that May has agreed with Brussels.
"We need to revoke Article 50 and if we can't do that, then we need the people's vote", she said, referring to the European Union legal mechanism Britain invoked for Brexit.
"At its logical conclusion, the risk of a general election increases because you potentially have a situation where parliament is instructing the executive to do something that is counter to what it was elected to do", he told the BBC. At the moment it looks like the deal would be unlikely to be approved.
Some of the party's key supporters of a "hard" Brexit that would see Britain leave the European Union even without a withdrawal deal planned to meet with May on Sunday afternoon at Chequers, the prime minister's country residence.
Two hundred coaches from around Britain were booked to take people to London for the march. "All this uncertainty will continue and of course that won't help with business investment decisions".