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: Finland basic income trial left people 'happier but jobless'
"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: Baldur's Gate Games, Neverwinter, Planescape: Torment Coming to Console in 2019
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: England's Chris Ashton gets rare Six Nations start
May will ask lawmakers on Thursday to reaffirm that they support her bid to renegotiate the backstop, a government source said.
- DUI suspect starts busting moves during roadside sobriety test
- January unemployment up from December, drops from start of 2018
- Clippers rally from 28 down, beat Celtics
- Drinking beer before wine won't prevent a hangover
- Drag Internet Explorer to the Trash. No, Really
- Android vulnerability lets hackers wreak havoc using, er, a PNG file
- Wells Fargo deals with tech issues for 2nd day, extends hours
- Trump says meeting with Xi before March 1 trade deadline is ‘unlikely’
- Kangana Ranaut’s Manikarnika finds a fan in Anupam Kher
- India vs New Zealand women's 3rd T20 at Hamilton