Well as a country we ARE presenting a divided and very disloyal image to the EU aren't we, and the cliff edge you refer too isn't Brexit per se, it's the inability of the country to come together in terms of political parties and the general population to get the best deal possible for the benefit of all.
Has Vince Cable or anyone else for that matter asked the EU if we can change our minds and remain? During an interview a couple of months ago with a female representative of the EU this question was asked and her response was to say 'no, the UK has voted for Brexit so Brexit will happen'.
If you were a member of the EU, would you want a country that voted to leave and then started tearing itself apart to have another referendum so it could change it's mind? If the vote had gone the other way and remainers were seeking to overturn a democratically made decision you'd be up in arms and rightly so.
Yes, you can fight Brexit if want too or you can accept that along with all of the benefits that living in this democracy offers, sometimes a decision will be made by the majority that you don't like and you can stop whinging and make the best of it.