Facing PMQs shortly before she departs for a Brussels summit to decide on a delay to Brexit, the Prime Minister was also told by a Tory backbencher that a “diluted” deal reached with Labour would be unacceptable.
Ian Blackford challenged Mrs May to say if she had ever offered a so-called People’s Vote in talks with Labour - “Yes or no?”
The Prime Minister said she did not support a second EU vote, but amid reports that MPs could be given the choice on whether to hold one as part of a compromise between the two main parties, she did not rule one out.
“My position and the government’s position on a second referendum has not changed,” Mrs May replied. “This House has rejected a second referendum two times.
“When we come to a deal, we will have to ensure that legislation goes through this house.
“Of course, it may be that there are those in this House who wish to press that issue as that legislation goes through, but my position has not changed.”
Mr Blackford pressed the issue, saying: "People can't have faith in a backroom agreement cooked up by two party leaders who don’t possess the ingredients to hold their parties together, nevermind hold these islands together.
“Scotland won’t be forced to accept what these two Brexit parties are preparing to serve up.
“There is no such thing as a good Brexit - and no such thing as a good Tory-Labour Brexit deal.”
He continued: “The Prime Minister must recognise the difference between what she sees as duty, and what the rest of us see as delusion.
“In her final days as prime minister, will she accept the EU’s offer of a long extension, accept that she has run out of road, and accept that the only choice now is to put this back to the people.”
To shouts from SNP MPs, Mrs May replied that it was “a little bit difficult for some of us in this House to hear week after week him stand up and say that the UK should stay in the European Union, when Scottish independence would have meant taking Scotland out of the European Union.”