Housing Secretary Robert Jenrick said delivering Brexit on October 31 was the "sole focus" of ministers, who he said would do "absolutely everything in our power" to meet the deadline.
It came as Brexit Secretary Steve Barclay said the Government wanted to get into "intensive negotiations" with Brussels - and confirmed that discussions were taking place with opposition MPs to win support for the PM's blueprint.
Mr Johnson meanwhile urged the EU to "grasp the opportunity" his plan provides but insisted Britain will pack its bags and walk out on October 31 - even if Europe does not "cheerily wave us off" with a deal.
Mr Jenrick told Sky's Sophy Ridge on Sunday: "Boris Johnson and this Government will do absolutely everything in our power to deliver Brexit on October 31.
"But we have no plan as to what might happen if Parliament doesn't allow us to get Brexit done on October 31 because we intend to get it done on that date and that's the sole focus of this Government at the moment."
Mr Barclay appeared to confirm that the Government would send a letter to the EU requesting a Brexit delay if a deal has not been agreed by October 19 - after Government lawyers told Scotland's highest civil court that Mr Johnson accepted the commitment.
Pressed on the pledge, Mr Barclay told BBC One's The Andrew Marr Show: "If a commitment is given to the court, you abide by it."
He also said the Government had been "talking to Members of Parliament across the House because I think many Members of Parliament want to avoid no-deal".
"And particularly those Members of Parliament in Leave constituencies who have voted against no-deal and voted against a deal three times, then they will need to be able to address this issue when they return to their electorate," he added.
"The problem is at the moment, we don't have a deal".
However, Labour's Lisa Nandy - who represents Leave-backing Wigan - said that while she could support a deal, the "problem is at the moment, we don't have a deal".
"What we've got is a proposal which stands virtually no chance of being accepted by the EU which creates two borders on the island of Ireland which is completely incompatible with existing international law and which rips up the workers' rights and protections and the environmental protections that we spent several months at the start of this year negotiating with the former prime minister," she told Sky.
"I would vote for a deal, but this is not a deal. This is a pre-election party-political broadcast from the Prime Minister, and the truth is that for all of the talk about getting Brexit done, we are further away from achieving a deal than we were two months ago when he became Prime Minister."
Shadow attorney general Shami Chakrabarti said it was important to see what Mr Johnson's deal might look like, and that Parliament must be able to scrutinise his proposals - though said his current plan "cannot get through".
She said, however, that if a deal was approved by Dublin and Brussels, it would be something that would be "more likely" to pass Labour's tests.