The SNP Westminster leader urged Boris Johnson to scrap the deadline and introduce automatically granted settled status for EU citizens living in the UK.
Speaking during Prime Minister’s Questions on Wednesday, Mr Blackford pointed out the Prime Minister had promised to do so.
He said: “Less than two years later, hundreds of thousands of EU nationals have been left in limbo, including thousands of children.
“While the settlement scheme deadline falls today, we know there are hundreds of thousands of unprocessed cases.
“It is simply unacceptable that their rights will be diminished by the failures of this government.
“Will the Prime Minister honour his word – give certainty – and scrap the disastrous settled status deadline before we face another Tory Windrush scandal?”
The Prime Minister insisted it was “fantastic” that 5.6 million people had already applied.
He said: “The most important thing for anybody who hasn’t applied is to get their application in today.”
Mr Blackford responded by accusing the UK Government of creating a backlog of “hundreds of thousands” of cases before hitting out at delays.
He continued: “Overnight thousands of our friends and neighbours could become illegal immigrants.
“They are living in fear for their jobs, their families, their livelihoods – and all because this Prime Minister won’t keep his word.
“We know all too well the experience of this government’s Home Office – dawn raids, vulnerable people deported, a hostile environment for the Windrush generation.
“Will the government now do the right thing – scrap the deadline and introduce automatically granted settled status?
"Or will the Prime Minister’s legacy be the ridiculous removal of our NHS staff, our local community workers, our teachers and many more who have made their homes here?”
Mr Johnson dismissed the accusations, insisting the scheme was an “outstanding success”.
He explained: “It’s five years now since the Brexit referendum. We’ve funded 72 organisations to help vulnerable EU citizens understand what their rights are and make the applications.
“Anybody applying within the deadline will of course have their case dealt with and I urge them to get on with it.”