Simon Hart said he had been given an amazing opportunity
The government is to add a new clause to the Brexit bill to rule out any extension to the transition period beyond the end of next year.
The post-Brexit transition period - due to conclude in December 2020 - can currently be extended by mutual agreement for up to two years.
But an amended Withdrawal Agreement Bill the Commons is set to vote on this week would rule out any extension.
Critics say this raises the chance of leaving the EU without a trade deal.
The UK is set to leave the EU on 31 January, more than three and a half years after the public backed Brexit in a referendum.
Soon after, the two sides will begin talking about their future economic relationship, including controversial areas such as fishing rights, consumer and environmental standards and financial services.
Trade deals typically takes many years to conclude but senior Cabinet Minister Michael Gove insisted both the UK and the EU were "committed" to reaching an agreement by the end of 2020 in order to avoid disruption to business.
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He also promised Parliament would be able to scrutinise the Withdrawal Agreement Bill "in depth".
Shadow Brexit secretary Sir Keir Starmer said the move was "reckless and irresponsible" and he argued that Prime Minister Boris Johnson was "prepared to put people's jobs at risk".
Liberal Democrat interim leader Sir Ed Davey said: "The only way Johnson can meet the December 2020 timetable is by giving up all his previous promises to Leave voters and agreeing to all the demands of the EU."
Downing Street has said the government plans to ask the new Parliament to have its first debate and vote on the withdrawal agreement - the legislation needed to ratify Brexit - on Friday.
With a majority of 80 following Thursday's general election, Mr Johnson is expected to get the bill into law with few changes in time for the UK to end its EU membership on 31 January.
'Cautious'
The government will then have until the end of the transition period on 31 December to negotiate a free trade agreement with Brussels before the trade relationship defaults to World Trade Organization (WTO) terms.
Senior EU figures, including the bloc's chief negotiator Michel Barnier, are sceptical that a deal can be agreed within that time.
Mairead McGuinness, the Irish politician who is First Vice-President of the European Parliament, said the fact the UK was looking to diverge from EU rules and standards in some areas, rather than move closer, would make the process "more complicated".
"We're all a bit cautious about whether it can effectively be completed within an 11-month period," she told BBC Radio 4's World at One.
So, the government is going to pass a law to stop itself doing something that it had already promised not to do.
On the surface, that doesn't change much.
Because the decision on whether to extend the transition period lies with the prime minister anyway, not with Parliament.
And with his new majority, Mr Johnson knows his critics can't do anything to force his hand.
But as a statement of intent, this announcement is important.
By reaffirming Mr Johnson's guarantee that the transition period will not be extended, it suggests there will only be enough time to agree a pretty basic trade deal which would leave many important issues unresolved.
That means a quick 'zero tariffs zero quotas' deal on goods could be done, as long as the UK is prepared to sign up to the EU's main conditions.
They include the UK sticking with EU rules on environmental and social policy, and on state aid for companies.
Such an agreement wouldn't get rid of all border checks, though, and it wouldn't do anything for the services sector.
The PM could of course change his mind again - he's done that before.
But this is also a warning for businesses - they could be in for a bit of a bumpy ride at the end of next year.
As well as ruling out an extension, the Independent reports that the amended withdrawal agreement may omit previous "provisions to ensure that workers' rights were not weakened after Brexit".
Mr Gove said workers' rights would be "safeguarded" in separate legislation, adding that the government wanted to make sure the Withdrawal Agreement Bill passes through Parliament "cleanly and clearly".
But shadow chancellor John McDonnell said the government would "sacrifice our basic rights and certainty for business at the altar of turning the UK into a Trump-supporting tax haven".
And Labour's Barry Gardiner said his party would be less likely to support the bill if clauses on workers' rights and the environment were removed.
Currently, if trade talks are progressing more slowly the UK and EU could agree - by July - to extend the post-Brexit transition period by one or two years.
But on Friday, the prime minister intends to expunge this clause from his Withdrawal Agreement Bill, and instead explicitly rule out any extension.
This is designed to underline to those Leave voters who have backed his party for the first time that he is determined to deliver Brexit - and he wants to quash speculation that he would be prepared to go for a deal that keeps the UK in close step with Brussels.
Government sources say that having a hard deadline will also focus the minds of both sets of negotiators on achieving a deal.
With Labour losing swathes of seats in their heartlands, Boris Johnson will claim that the opposition haven't learned any lessons if they vote against his Brexit legislation.
The prime minister promised during the general election campaign that he would not seek an extension to the transition period - persuading Brexit Party leader Nigel Farage to stand down candidates in Tory seats.
Sam Lowe, from the Centre for European Reform think tank, told BBC Radio 4's Today programme that Mr Johnson's move was "slightly performative" and its effect would be "largely domestic".
"It is a firmer deadline but of course there is still some flexibility," he said.
Mr Lowe said a December 2020 deadline could help the PM manage his own party when it comes to making concessions to the EU.
What will happen this week?
Tuesday
Proceedings begin when MPs gather for their first duty: to elect the Speaker, Sir Lindsay Hoyle, who replaced John Bercow in November. Technically, MPs can hold a vote on this motion but this has never happened in practice.
Later in the day, the Speaker will begin the process of swearing in MPs, who are required to take an oath of allegiance to the Crown, or, if they object to this, a solemn affirmation. Those who speak or vote without having done so are deprived of their seat "as if they were dead" under the Parliamentary Oaths Act of 1866.
Two to three days are usually set aside for this process.
Thursday
The state opening of Parliament. The Queen's Speech is the centrepiece of this, when she will read a speech written by ministers setting out the government's programme of legislation for the parliamentary session. A couple of hours after the speech is delivered, MPs will begin debating its contents - a process which usually takes days.
Friday
Depending on how rapidly Boris Johnson wants to move, the debate on the Queen's Speech could continue into Friday.
The government will introduce the Withdrawal Agreement Bill to Parliament.
MPs in the previous Parliament backed Mr Johnson's bill at its first stage but rejected his plan to fast-track the legislation through Parliament in three days in order to leave the EU by the then Brexit deadline of 31 October.
After the debate on the Queen's Speech is concluded, MPs will vote on whether to approve it. Not since 1924 has a government's Queen Speech been defeated.
