With senior Tories including Brexit secretary Dominic Raab and work and pensions secretary Esther McVey having quit the UK Government over their opposition to the deal, Ms Sturgeon said she is “not confident that the Prime Minister will be in office by the end of today”.
The Scottish First Minister warned the agreement - which was backed by Mrs May’s Cabinet on Wednesday night but which then sparked a raft of resignations - would have “real implications for jobs and living standards and investment in Scotland”.
That is because the Brexit deal makes separate provisions for Northern Ireland, to prevent a return to a hard border with Ireland.
In fiery exchanges at First Minister’s Questions in Holyrood, Ms Sturgeon: “Scotland faces being taken out of the European Union against our democratic wishes, Scotland faces being taken out of the single market against our economic wishes, and now we face being put at a competitive disadvantage to Northern Ireland.
“That’s what the Tories are presiding over.”
In a telephone call with Mrs May on Wednesday night, the SNP leader said she had told the PM the UK Government has “ignored Scotland, sidelined Scotland, cast aside Scotland’s interests”.
She said Scottish Secretary David Mundell should join the list of Cabinet resignations if he had the “backbone” to do so - recalling how last month he and Scottish Conservative leader Ruth Davidson said they would quit if the Brexit deal threatened the “integrity of the UK”.
Ms Sturgeon also told MSPs she has “no doubt” Scots will get another chance to vote on independence - adding the time of another ballot will depend on how this “whole sorry saga plays out”.
Conservative interim leader Jackson Carlaw, who is standing in for Ms Davidson while she is on maternity leave, had demanded Ms Sturgeon rules out another vote on leaving the UK.
He said: “We need a First Minister acting for all of Scotland, isn’t it time she acted in the national interest, not the nationalist interest?
“With everything that is going on will she now take her threat of a second independence referendum, and all the disruption that could cause, off the table?”
Mr Carlaw argued if separate provisions are made for Scotland as well as Northern Ireland, it would effectively result in a “border at Berwick”.
Ms Sturgeon told him: “All I’m asking for is if Northern Ireland is to get a separate deal, for very good reasons, I support that, then Scotland should not be placed at a disadvantage as a result of that.”
Scottish Labour leader Richard Leonard said the resignations on Thursday morning show “Theresa May’s Government is falling apart before our very eyes”.
He said: “It’s my firm belief that this deal will not be agreed to by the House of Commons, that this shambolic Tory Government needs to go, and that the people need more than anything a general election as a matter of urgency.”
Ms Sturgeon insisted rejecting the current deal should not necessarily mean a no-deal Brexit.
“I hope no party in the House of Commons falls for the Prime Minister’s spin that it’s a case of accepting a bad deal for fear of no deal,” she said.
“No deal is not inevitable if this bad deal is voted down.”
Scottish Green leader Patrick Harvie argued the public “must ultimately be given the chance to kill off Brexit in a People’s Vote”.
But he added: “If the last two years have made anything clear, it’s that Scotland’s future is best secured as a full, independent EU member state.”
He asked the First Minister, who has delayed making a statement on a second independence referendum, to “confirm to us that Scotland will be given that choice, and when”.
Ms Sturgeon said she would do that when there is “clarity” on Brexit.
She said: “Obviously now we have seen the terms of the deal.
“It remains to be seen whether that makes it to a vote in the House of Commons over the next couple of weeks. We will see how that whole sorry saga plays out and then I will undertake that commitment as I said I would.”