According to The Economist, Feb 23, reporting on a YouGov survey in December, 49% support Remain, and that number hasn't changed much. However, the 51% who don't support Remain support a variety of different proposals. To me it seems highly unlikely that any particular proposal would beat Remain in a choice between those two options. Remain is the Condorcet winner.
That "61%" is probably about right for what would you'd get for a two-way referendum between Remain and No Deal, or between Remain and May's Deal, but if you were to repeat the Remain-Leave referendum (which would be an insane thing to do - it was madness the first time), I wouldn't be surprised if Leave would win again, by a narrow margin.
"Well, if you knows of a better 'ole go to it"?