Mr Barclay said the Withdrawal Agreement Bill would deliver on the "overwhelming mandate" his party had been given by voters to take the UK out of the EU on 31 January.
The bill is being scrutinised in the Commons and covers citizens' rights, customs arrangements for Northern Ireland, "divorce" payments to the EU as well as the proposed 11-month transition period.
It is expected to comfortably pass its remaining stages in the House of Commons by Thursday before moving to the Lords.
MPs backed the bill at its first stage in late December and Mr Barclay expressed confidence in negotiating a trade agreement with the EU in the 11-month transition but did not rule out a no-deal arrangement.
“We are delivering on these promises that the British people have entrusted us to deliver and the Opposition is only interested in further delay and disruption," said Mr Barclay.
It comes as Clause 33 of the European Union (Withdrawal Agreement) Bill seeks to prohibit ministers from trying to extend the implementation period, which would begin once the UK leaves, this move has received a backlash from opposition MPs.
A number of clauses tabled by opposition parties, largely focused on citizens' rights, fell this evening.
Labour’s new clause five, which aimed to provide the right of permanent residence to all EU citizens who are resident in the UK before exit day, was defeated by with 252 votes for and 342 against.
MPs rejected the SNP’s new clause 18, linked to citizens’ rights, with 255 votes for and 341 against it.
The Liberal Democrats’ new clause 34, which sought to establish a right to appeal settled status decisions, was also voted down with 251 for votes to 343 against.
Earlier, Labour said the Withdrawal Agreement is a “bad deal” for the UK and called on the Government to come forward with proposals to show how it will avoid the “catastrophe of no-deal at the end of this year”.
Green MP Caroline Lucas (Brighton Pavilion) also questioned why ministers were seeking to “tie the hands of the Government in such an unnecessary way” with the Clause 33, by having an “arbitrarily short time of 11 months” for the transition period when the trade talks may need a little extra time.
Speaking as MPs assessed the Bill at committee stage, Labour former minister Hilary Benn also told the Commons: “(Mr Barclay has) expressed enormous confidence that a deal will be done by December.
“Can I just test that confidence a little further, would he give the House an assurance today that there is no prospect whatsoever of the UK leaving without an agreement in December of this year?”
Mr Barclay replied: “I would hope he as a democrat would want a Government to adhere to its manifesto. The reality is on December 12 the British public voted in overwhelming numbers to get Brexit by done by January 31 and to conclude the implementation period by December 2020 so we can look forward to a bright future as an independent nation.
“Page 5 of our manifesto explicitly states that we will negotiate a trade agreement by next year, one that will strengthen our union and we will not extend the implementation period beyond December 2020.
“We are delivering on these promises that the British people have entrusted us to deliver and the Opposition is only interested in further delay and disruption.”
Labour MP Chris Bryant (Rhondda) earlier said he has “an anxiety” a security deal will not be achieved by December 2020, but Mr Barclay replied that after the election result “now, with absolute clarity on the timetable, we are working to, the UK and the EU will be able to get on with it”.
Shadow Brexit minister Paul Blomfield said Labour would not move its amendment designed to avoid a no-deal scenario by extending the transition, but also claimed the Tories lacked majority support for its plans.
He said: “I think members opposite also ought to recognise that although under our electoral system the arithmetic in this place is very clear, the majority of the British people voted for parties that weren’t of the mind of the Conservative manifesto and who wanted to give the British public a further say.
“And I say that only not to deny the reality of the voting in this place, but that the members opposite ought to have some caution about the way that they approach this issue and claim authority from the British people.”
Mr Blomfield said Labour “intended to provide an opportunity for the Government to come back to this House with their proposals, perhaps at report stage, on how we avoid the catastrophe of no-deal at the end of this year.”
Liberal Democrat former minister Alistair Carmichael warned Mr Barclay that his words “will come back to haunt him” if the UK does not conclude a deal by December 2020.
However, Conservative former minister Sir John Redwood hit out at those criticising the timetable and also told the debate: “I don’t think we have to pay for a free trade agreement, I think it’s massively in the interests of the rest of the European Union – because they sell us more than we sell them.
“But we have to be firm otherwise they’ll walk all over us again and demand more concessions.”
The Government wants the Bill to complete its remaining stages in the Commons by the end of business on Thursday and it would then go to the Lords next week, with ministers confident it can conclude its passage through Parliament in time for it to be ratified by the European Parliament by the end of the month.
That would mean the UK leaving the EU on January 31, with a deal in place covering citizens’ rights, the Irish border and Britain’s “divorce bill” of about £30 billion.
Senior EU figures, including chief negotiator Michel Barnier, have warned that completing a trade deal in such a tight time-frame is likely to prove impossible.