possibly people voted for Cameron for many reasons, one of them being he promised the country a referendum on Europe.Which, to the credit of him and the Conservative Party they have stuck to , even though he himself wants us to stay in.
Lies is perhaps pushing it, but the Remain Group have put all sorts of doom mongering stuff that is merely speculation out there for the public to sniff at.
If a referendum with a chance of people voting to leave the EU would be so terrible, I don't think that any PM would promise it, even to heal rifts within that Party.