The idea of Brexit based on a customs union is “incredibly problematic”, Liz Truss has said, as Theresa May faces increasingly open cabinet splits before a new round of indicative votes which could point the way towards a softer departure.

With MPs expected to vote on Monday evening on some of the eight tabled proposals, the chief secretary to the Treasury said she vehemently opposed the idea of the government backing a customs union if MPs voted for the option.

The justice secretary, David Gauke, said on Sunday he did not think it would be “sustainable to ignore parliament’s position” if MPs ruled out a no-deal Brexit and opted for a customs union.

Play Video 1:03 David Gauke: 'I don’t think it’s sustainable to ignore parliament’s position' – video

However Truss said a customs union was not good for UK trade or foreign policy and that if May definitively backed that option or a no-deal departure she could lose a large contingent of ministers from either the leave or remain sides of her cabinet.

“I think it’s incredibly problematic, the idea of a customs union,” Truss told BBC Radio 4’s Today programme. “It would mean that control of our trade policy sat with the European Union whilst we were no longer a member, where we would have no influence. That would have consequences for our foreign policy, we wouldn’t be able to strike independent trade deals.”

Asked if this meant she would quit the cabinet if a customs union became the policy, Truss said: “I don’t go round threatening to resign, I don’t think that is appropriate or right. I will very strongly argue against that. I will be arguing that we should be following an alternative path.”

Amid the open bickering, comments emerged overnight in which the Conservative chief whip, Julian Smith, said May faced “the worst example of ill discipline in cabinet in British political history”.

In highly unusual comments for someone holding his post, Smith told a BBC documentary about Brexit that after losing her majority in the 2017 election, May should have possibly laid the way for an inevitable softer Brexit.

“The thing that people forget is that the Conservative party went to get a majority in order to deliver Brexit, [and] failed to get a majority,” he said. “The government as a whole probably should just have been clearer on the consequences of that. The parliamentary arithmetic would mean that this would be inevitably a softer type of Brexit.”

Attention on Monday will focus on the second series of non-binding votes, the next stage of a process led by the veteran Conservative MP Oliver Letwin in which the Commons has taken control of parliamentary business.

In the first series of eight votes last week, none of the options commanded a majority, although a customs union proposal fell just six votes short.

A similar palette of options has been tabled for Monday, with the Speaker, John Bercow, due to select a number of them for votes. The focus will mainly be on whether a customs union or “common market 2.0” can gain more support, as well as a proposal to put any final deal to a confirmatory referendum.

Truss said last week’s votes had left her sceptical about whether MPs could find a way forward. “It’s not like there’s this brilliant plan out there that everyone wants to vote for,” she said. “If you look at the parliamentary arithmetic now, it’s not clear that something like a customs union actually commands support.”

She said the solution “lies in modifications to the prime minister’s deal”, which was voted down for a third time last week, albeit in a modified form, with the withdrawal agreement separated from details of the planned future relationship with the EU.

“I’m going to sound like a total optimist here, but it was less than we lost by last time, and we are seeing people coming on board. I think we need to carry on looking at how we get the support for that deal,” Truss said.

There is signifiant speculation May could bring her plan back for a fourth vote later in the week. However, the Democratic Unionist party, whose 10 MPs would be vital for it to pass, have consistently maintained they cannot back it because of the backstop provision for the Northern Irish border.

On Monday the DUP’s Brexit spokesman, Sammy Wilson, told the BBC his party would “vote it down 1,000 times” because the implications for Northern Ireland were far too serious.

“First of all, it would take us away from the country that we fought to stay part of,” he said. “And secondly, it would break us away from the economy on which we are dependent.”

Truss said that if May’s deal could not get through she would support no deal rather than risk no Brexit, saying the nation was well-prepared for such an option. “I don’t have any fear of no deal,.”