There are “no ideal choices” over the Brexit deadlock, Justice Secretary David Gauke has said.
The prime minister is considering her next move after her withdrawal plan was defeated by MPs for a third time.
On Monday, Parliament will hold an indicative vote on Brexit alternatives. A customs union with the EU is thought to be the most likely preference.
Mr Gauke warned it would “not be sustainable” to ignore MPs if they voted for a softer Brexit.
Speaking on the BBC’s Andrew Marr Show, he argued the prime minister’s deal was “the best outcome”.
But he added: “Sometimes you do have to accept your second or third choice to avoid an outcome you consider to be even worse.”
Labour’s deputy leader Tom Watson said it would be “inconceivable” if there was a general election and his party did not include a new referendum in its manifesto.
Following the UK’s vote to leave the EU in 2016, Theresa May negotiated a withdrawal deal with the EU.
Although European leaders agreed to the plan, Mrs May has yet to get the deal approved by Parliament.
The prime minister has until 12 April to seek a longer extension to the Article 50 process if the UK is to avoid leaving without a deal.
The prime minister’s deal is currently opposed by parties including Northern Ireland’s DUP – which the government relies upon for support – as well as a group of her own MPs.
Tory Brexiteer Steve Baker, who resigned as a Brexit minister over the PM’s handling of negotiations, wrote in the Sunday Telegraph that Mrs May’s deal “cannot be allowed to go through at any cost”.
However he admitted deciding to vote for it on Thursday before being talked out of it by friends.
On Monday, MPs have a non-binding vote on a series of options designed to test the will of Parliament. The intention is to see what outcome, if any, commands a majority.
None of MPs’ eight proposed options secured a majority in the first set of indicative votes on 27 March, but those which received the most were a customs union with the EU and a referendum on any deal.
A customs union would allow businesses to move goods around the EU without checks or charges – but membership would bar the UK from striking independent trade deals after Brexit.
Mr Gauke said he was in favour of leaving the customs union, arguing that it would “better reflect the way the country voted in 2016”.
Membership of a customs union would breach the Conservative’s 2017 manifesto.
But he acknowledged that his party “does not have the votes to get its manifesto position through the House of Commons at the moment”.
“We are in an environment where it is not just about going for your first choice,” he added.
Mr Gauke reiterated his opposition to a no-deal Brexit, warning he would leave government if such a policy was pursued.
A no-deal Brexit would mean cutting ties with the European Union immediately and defaulting to World Trade Organisation rules for trade.
Tom Watson said there was an “emerging consensus” among Labour MPs.
He said: “Whatever the deal looks like – and we understand there has to be compromises – if it’s underpinned by a People’s Vote that is the way we can bring the country back together.”
