The withdrawal deal, which the two sides have reached, has not yet been approved by United Kingdom lawmakers, with the Irish border backstop being the stumbling block.
Communities Secretary James Brokenshire said: "I think that gives that sense of timetable, clarity and objective on what we are doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has".
In the vote this week lawmakers are set to vote on amendments that could limit May's options and give parliament a broader say over the Brexit process.More news: Jennifer Tilly reacts to Child's Play remake: 'Ummm
"We would have a hard border, a very hard border, no-deal Brexit means a really hard border between the north and south of Ireland".
Sir Keir earlier said his plan was necessary to put a "hard stop" to Mrs May "running down the clock" before the March 29 deadline.
British Prime Minister Theresa May will pledge this week to give parliament another chance to voice their opinions on Brexit by February 27 as she tries to buy more time to negotiate a new deal with the European Union.
"We can't allow that to happen".More news: French 'Yellow Vest' Marches Continue for 13th Weekend
Deputy leader of the opposition Labour Party Tom Watson tells the BBC "we're now at the point where we can have meaningful talks to get a deal between the main political party leaders, or the only way to break the impasse is a public vote, and that remains our policy".
The former Labour prime minister, a vocal advocate of Britain remaining in the European Union, also said a second referendum could still happen, "when people see what the true Brexit alternatives are".
Deputy Labour leader Tom Watson told the Andrew Marr Show that if those conditions were not met then his party could move to supporting a second referendum.
Speaking on Sky News's Sophy Ridge on Sunday, Blair said: "No one could responsibly propose (a no-deal Brexit)".More news: Acting Attorney General Matthew Whitaker Grilled by the House Judiciary Committee
May will ask lawmakers on Thursday to reaffirm that they support her bid to renegotiate the backstop, a government source said.
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