Tory MPs have launched an assault on David Cameron
Brexit campaigners Michael Gove and Boris Johnson wrote an open letter in The Sunday Times saying a manifesto pledge to cut net migration to tens of thousands is not realistic.
"This promise is plainly not achievable as long as the UK is a member of the EU and the failure to keep it is corrosive of public trust in politics," the letter reads.
The letter comes as a survey in The Observer states that 88% of the UK's top economists say leaving the EU would be damaging.
A Downing Street source told the BBC that the letter is a "transparent attempt to distract from the fact that the overwhelming majority of economists and businesses believe leaving the single market would be disastrous for jobs, prices and opportunities for people."
Gove is a member of the prime minister's cabinet and a former education minister, while Johnson is a well known Conservative and London mayor until recently.
Net migration rose to 333,000 in 2015, according to Office for National Statistics figures. The government is aiming to reduce this figure to less than 100,000 a year. EU-only net migration represented 184,000 for the same year, equalling its record high, while non-EU migration represented 188,000.
Several other MPs put pressure on Cameron on Sunday.
Tory MP Nadine Dorries said during ITV's "Peston on Sunday" show that she has submitted a letter calling for the Prime Minister to step down.
"My letter's already in," she said. "If the Remain camp wins by a large majority, let's say 60:40, then David Cameron might just survive. But if Remain win by a narrow majority or if Leave - as I certainly hope, I think - will win he's toast within days. I always have backed the only politician I think in Westminster who has a proven track record of achievement and that's Boris Johnson."
When asked if there was anything David Cameron could do to win back her support, Dorries said:
Employment minister Priti Patel said on Sunday that the leaders of the remain campaign live a "luxury lifestyle" that means they can't understand the concerns that normal people have about immigration.
Backbench MP Andrew Bridgen, a well known Eurosceptic, told BBC Radio 5 about how he knows of at least 50 Conservative MPs who are already preparing to go for a vote of no-confidence in David Cameron if the result on the 23 June is not decisive.