The argument for a “Norway-plus” compromise on Brexit is winning the day at Westminster, according to Scotland’s first minister, Nicola Sturgeon, who has committed her Scottish National party MPs to supporting the soft option provided it can command a House of Commons majority.

Sturgeon said the alternative framework for the UK, which the Scottish government first advocated in December 2016, “may have met with a disinterested rejection from the UK government but … is gathering support from others. The arguments that the Scottish government has been making are actually winning the day.”

Almost half of Theresa May’s cabinet have held talks to weigh up the possibility of backing the Norway-inspired alternative – in which the UK could join the European Free Trade Association and maintain a customs arrangement with the EU if parliament rejects the prime minister’s EU withdrawal deal next month.

Dismissing May’s deal as “damaging to the Scottish people and therefore unacceptable to the Scottish government”, Sturgeon said on Tuesday that the SNP would support whichever of two alternatives could command a cross-party majority.

“The first option is the compromise position of single market [and] customs union membership … The second option is another referendum on EU membership with the option to remain in the EU on the ballot paper. The SNP will support whatever option can command a majority, though it will always be our preference to look at options that see us remaining in the EU,” she said.

Speaking as the Scottish government published an analysis that estimated Brexit would cost £1,600 per person across Scotland, Sturgeon refused to be drawn on when she would divulge her plans for another Scottish independence referendum.

Admitting she was repeating the position she had taken over the past few months, the SNP leader said: “The case for the people of Scotland to determine their own future has never been stronger, and I will return to that matter when we know which approach to Brexit the Commons chooses.”

Sturgeon went on to challenge May to include her in the live television debate the prime minister has called for, which is currently proposed as a head-to-head with the Labour leader, Jeremy Corbyn.

“I hope this changes in the not-too-distant future, but as of now, Jeremy Corbyn is not an advocate for remain, for a ‘people’s vote’. He’s not even an advocate for a single market [and] customs union compromise, so the danger is a debate between Theresa May and Jeremy Corbyn is simply a debate between two versions of Brexit that are only different around the margins,” she said.

“To Theresa May I would simply say, what are you scared of allowing people advocating these different options to take part in the debate? If you’re confident in your position, there should be nothing in that that worries you.”

She said she was cautiously optimistic Labour would clarify its position in favour of a second referendum, and accused May of “squandering valuable time” by refusing to accept that her deal was highly unlikely to get through a Commons vote.

Sturgeon said the prime minister was trying to “cover up” her failure to provide the country with certainty, saying her political declaration suggested there would be “years of further negotiations on [the] future relationship”.