Communities Secretary James Brokenshire said Sunday that parliament would get another chance to pass judgment on May's Brexit plan "by no later than February 27".
The prime minister is due to update parliament this week on the progress of her latest talks with the EU.
"I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deal?"
On Wednesday, Mrs May will ask MPs for more time to get legally-binding changes to the controversial Northern Irish backstop, which she believes will be enough to secure a majority in Parliament for her deal.More news: Riot police clash with yellow vest protesters in Paris
Labour's Brexit vote brigade An amendment, to be tabled by the Labour front bench and pushed by the shadow Brexit secretary Sir Keir Starmer may struggle if it does not attract cross-party support or get picked up in another guise by a Conservative backbencher.
Businesses and governments are on edge because Britain is just weeks away from its scheduled departure from the European project after 46 years and still has no firm arrangements in place.
"We can't allow that to happen", Sir Keir told The Sunday Times. "There needs to be a day when Parliament says that's it, enough is enough".
The BBC has reported that Mrs May will offer MPs another vote on amendments to her Brexit withdrawal deal if an agreement has not been reached by the end of February.
In early November 2018, former British PM Tony Blair called for a second referendum on Brexit, urging the country's parliament to turn down any divorce agreement between London and Brussels and let United Kingdom citizens decide as each option would have negative consequences.More news: GRAMMYs 2019: Dolly Parton's Star-Studded Performance and Tribute
There are fewer than 50 days until Brexit.
Truss also rejected calls for Brexit to be delayed to allow further time for negotiations.
The opposition Labour party has denounced May's strategy as time-wasting aimed at forcing parliament to vote through a deal at the last moment. The prime minister is now in talks with Brussels to seek these changes to the backstop.
The UK's exit from the bloc may lead to a return of a hard border between the Republic of Ireland and Northern Ireland in potential violation of the 1998 Good Friday Agreement, which specifically stipulates that no physical border should exist between the two sides.
"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".More news: Pep Guardiola Can't Believe Sergio Aguero's Open Goal Miss