The First Minister was speaking as the UK Government continues to deal with the fall-out from an agreement signed by Mrs May at Chequers on Friday, with Boris Johnson becoming the second Cabinet member in 24 hours to resign in protest.
“The thing that has the most chance of commanding a majority is single market and customs union membership,” Ms Sturgeon told BBC Radio 4 today.
“I’m not going to have my party vote for something I know would be damaging - more damaging than necessary - for the Scottish economy. We will continue to argue for the compromise we think is right and stand up for common sense.”
The SNP leader added: “I lead a country that did not vote to leave the EU.”
The SNP’s Westminster leader will later today call for the UK Government to “press the reset button on its damaging austerity agenda”.
In a keynote speech in London, Ian Blackford will outline the contrast between policies implemented by the SNP Scottish Government and the UK government, and the challenges and threats facing the devolution settlement.
Meanwhile, senior Tories have this morning rallied in support of Mrs May.
Asked if he thought the PM would face a leadership challenge, former defence secretary Sir Michael Fallon told the BBC: “No I don’t. I think, over all, colleagues should think very, very carefully about that.
“That’s the last thing we need at the moment.
“We now have a plan. There is now an agreed plan on the way forward.”
Sir Michael was dismissive of Mr Johnson’s claim the Brexit dream is dying, saying: “He uses this phrase the dream is over, but in the real world, I mean dreaming is good, probably for all of us, but we have to deal with the real world.”
Under party rules, 48 Tory MPs - 15 per cent of the party’s 316-strong representation in the Commons - must write to the chairman of the backbench 1922 Committee, Sir Graham Brady, to trigger a no-confidence vote.