The Conservatives have maintained a commanding lead over Labour in the opinion polls ever since Theresa May called for a general election to be held on 8 June.
But an Ipsos MORI survey, of more than 1,000 voters between 26 and 28 April, found that two in three (68%) respondents thought that the party would fail to deliver on one of its flagship pledges – to cut net migration to "tens of thousands".
"May shows little sign of overturning the public's long-held scepticism that immigration can be brought down to the 'tens of thousands,'" said Kully Kaur-Ballagan, head of race, faith and cohesion research at Ipsos MORI.
"Our data also shows that, even though many are concerned about immigration, the public does differentiate between different types, while remain and leave voters are still divided in their views."
The controversial "tens of thousands" pledge was first made by David Cameron, with Amber Rudd, who succeeded Theresa May as Home Secretary, recommitting her government to it last year.
The Tories have consistently failed to meet the target and the latest Office for National Statistics data estimated that net migration hit more than 273,000 in the year to September 2016.
The Ipsos MORI poll found that one in five (20%) voters thought 100,000 or above would be a sustainable level of migration, whilst almost half (49%) of respondents thought it should be 100,000 or less and 30% were unsure.
Labour MP and Open Britain supporter Chuka Umunna said the research showed that the Tories should drop the "tens of thousands" target.
"The public are right to be sceptical about Theresa May's chances of cutting annual net migration to the tens of thousands. The government have spent seven years trying, and they are no closer now than they were in 2010," he said.
"This policy is not just unachievable, it is damaging to our economy and public services. This poll shows the public value the European citizens who work in our health service, our agricultural sector, our universities and tech businesses. For Britain to continue to grow and create jobs, we will need these hard-working people more than ever.
"It is time for the Government to drop the target and implement an immigration policy that serves our economic needs, rather than undermining them."
The issue is expected to be major part of the two-year-long Brexit talks between Brussels and the UK. May has promised to curb immigration and break from the EU's free movement rules.
The latest general election poll from Ipsos MORI, of more than 1,000 voters between 21 and 25 April, gave the Conservatives a 23 point lead over Labour (49% versus 26%).