The survey, for the Royal College of Nursing (RCN), also found that the majority of people think there are too few NHS nurses to provide safe care for patients.
The union has warned that nurses could take industrial action unless the Government lifts the long-standing 1 per cent cap on pay rises in the public sector.
Speculation is mounting that Prime Minister Theresa May is preparing to end the cap for nurses, teachers and other public sector workers later this year.
The RCN is holding a demonstration against the cap on Wednesday in Parliament Square in London.
Its new YouGov poll of 1,624 members of the public found 72 per cent believe there are too few nurses to provide safe care to patients.
Some 68 per cent said nurses are underpaid, including 58 per cent of those who voted Conservative in the last election.
Meanwhile, 57 per cent of people said they would be willing to pay more tax to make the NHS safer – including a majority of Tory voters.
Janet Davies, chief executive of the RCN, said: “The public can see the shortage of nurses for themselves.
“Ministers are significantly out of touch with public opinion. They should heed this warning, scrap the pay cap and help to recruit thousands more nurses for a safer NHS.
“Experienced nursing staff are leaving in droves – not because they don’t like the job, but because they can’t afford to stay, while the next generation do not see their future in an under-valued profession.
“If the Government fails to announce a change of direction in the Budget, then industrial action by nursing staff immediately goes on the table.”
In May, almost eight out of 10 nurses polled by the RCN said they would be prepared to go on strike if the pay cap is not lifted.
Earlier on Tuesday, Transport Secretary Chris Grayling said the Government wants to “provide people with additional pay” when the economy allows for it.
He told Radio 4’s Today programme: “We have listened to the lessons from the general election campaign, we look carefully at the issues we face as a country, but when it comes to these big financial decisions they are things that have to wait for the Budget.
“All of us want to see a situation where we can provide people with additional pay, additional job opportunities, but in order to do that we have to have a strong, growing economy.”
The Treasury is due to send out letters within weeks setting out the remit for public sector pay review bodies for next year’s pay round.