Unfortunately there is already a precedence for Governments to call a second referendum on EU votes they don't like, and a couple have just ignored them, Ireland was first with Lisbon Treaty, followed by France, Denmark and Greece, now it would seem the UK.
Most Polls before the referendum showed clearly most asked wanted to Remain, the actual vote proved different, so I would discount them as a barometer of public feeling.
A second referendum would do untold harm to the Political system whatever the outcome