Southern voters’ enthusiasm drops further if it means paying higher taxes to fund it, the survey indicates.
Sir Jeffrey said it “debunks” the idea that a united Ireland is inevitable.
The findings emerge in a survey conducted by the Red C polling agency, and published in today’s Business Post.
It canvassed attitudes to the constitutional question in the Republic, interviewing a random sample of 1,001 adults aged 18 and over online between November 19 and November 25.
The poll found 60% in the Republic would vote in favour of a united Ireland if a border poll was held immediately - broadly in line with previous surveys. One in four (25%) disagree, and 15% are unsure.
There is stronger support among younger people - 67% of 18-34 year-olds are in favour of a united Ireland, compared to 52% of those aged over 55.
The poll also found 62% of people in the Republic believe a border poll will happen within 10 years, with 23% disagreeing and 15% unsure.
The Good Friday Agreement states the Secretary of State should call a border poll if they see a majority in favour of a united Ireland.
Former Taoiseach Bertie Ahern has called for a referendum on a united Ireland to be held in 2028 to coincide with the 30th anniversary of the agreement.
However, support for a united Ireland falls if it comes at a cost to the public, the Red C poll suggests. It shows support dropping to 41% for a united Ireland if it meant paying higher taxes. Some 43% disagree with paying higher taxes while 16% were unsure.
People were asked would they be willing to change the current Irish flag to accommodate a new flag for a united Ireland - but there is strong opposition. Just 27% of people agree with this, while 59% are opposed, and 14% unsure.
And there is opposition to changing the Republic’s national anthem, Amhran na bhFiann (The Soldier's Song) in a united Ireland. Just 35% of people in the South are willing to change to a new anthem, with most (52%) opposed.
There is also reluctance for guaranteed unionist cabinet positions in a united Ireland government. Under half (39%) would support it, while 37% are opposed and 24% are unsure.
Just 45% of people in the Republic would be willing to support the continuation of the Stormont Assembly alongside the Dail in Dublin in a united Ireland. Another 32% disagree while 23% are unsure.
Responding, Sir Jeffrey said on Twitter: “60% support for united Ireland remarkably low for Republic. Drops to just 41% if people have to pay higher taxes which of course they will to fund public services, pensions and replace the NHS in NI.
“Debunks the idea that a united Ireland is inevitable. Let’s make Northern Ireland work.”