Jacob Rees-Mogg has said “compromise” is inevitable, as Boris Johnson tries to reach a new Brexit deal with the EU.
But the House of Commons leader said the PM could be “trusted” to deliver, and that the mood was “more positive” than it had been a week ago.
Parliament will meet next Saturday and vote on any deal achieved by the PM at a Brussels summit this week.
Labour said it would “wait and see”, but it seemed that so far “the Tories haven’t moved too far”.
Shadow business secretary Rebecca Long-Bailey told BBC One’s Andrew Marr Show the government’s plans would be “incredibly damaging to the economy”.
She urged Labour and other MPs not to support a deal that could “damage living standards”.
SNP leader Nicola Sturgeon told the same programme: “We will not vote for the kind of deal specified by Boris Johnson.”
The summit in Brussels on Thursday and Friday is seen as the final chance to get a Brexit deal agreed ahead of the 31 October deadline.
Meanwhile, talks between UK and EU officials are continuing on Sunday, with Mr Johnson due to update the cabinet on the progress of the “intense technical discussions” in Brussels later.
The EU’s 27 ambassadors are scheduled to meet later this evening and Michel Barnier, the EU’s chief Brexit negotiator, is expected to brief them on the talks.
The first Queen’s Speech of Mr Johnson’s premiership, delivered during the State Opening of Parliament on Monday, will see the government highlight its priorities, including on Brexit.
Home Secretary Priti Patel told the Andrew Marr Show there was much “speculation” about what would be included in any deal between the UK and EU.
She added: “Progress has been made by the prime minister.”
Asked about Labour’s stance, Ms Patel replied: “They are clearly playing politics. The British public want to ensure that we get Brexit done.”
Mr Rees-Mogg wrote in the Sunday Telegraph: “In the final stages of the Brexit negotiation, compromise will inevitably be needed, something even the staunchest Leavers recognise albeit unwillingly – but as a Leaver Boris can be trusted.
“He wants to take back control and has dedicated his political career to this noble cause. If he thinks the ship of state is worth an extra ha’porth of tar he deserves support.”
Mr Johnson’s revised proposals – designed to avoid concerns about a hard border on the island of Ireland after Brexit – were criticised by EU leaders at the start of last week.
However, on Thursday, Mr Johnson and Irish Prime Minister Leo Varadkar held talks and said they could “see a pathway to a possible deal”.
The Benn Act, passed by Parliament last month, requires Boris Johnson to ask EU leaders for a delay to Brexit if a deal has not been reached and agreed to by MPs by 19 October.
Liberal Democrat leader Jo Swinson told Sky News that, although the detail of any deal had yet to be confirmed, it looked “much the free-trade agreement type proposal that was put forward in November 2018 that the government’s own analysis showed would be catastrophic”.
She added that any deal should “be put to the public so they can have the final say”.
Labour leader Jeremy Corbyn said: “I think many in Parliament – not necessarily Labour MPs, others – might be more inclined to support it [if there was a referendum] even if they don’t really agree with the deal. I would caution them on this.”
Timeline: What’s happening ahead of Brexit deadline?
Monday 14 October – The Commons is due to return, and the government will use the Queen’s Speech to set out its legislative agenda. The speech will then be debated by MPs throughout the week.
Thursday 17 October – Crucial two-day summit of EU leaders begins in Brussels. This is the last such meeting currently scheduled before the Brexit deadline.
Saturday 19 October – Special sitting of Parliament and the date by which the PM must ask the EU for another delay to Brexit under the Benn Act, if no Brexit deal has been approved by Parliament and they have not agreed to the UK leaving with no-deal.
Thursday 31 October – Date by which the UK is due to leave the EU, with or without a withdrawal agreement.