There will be people in parliament who are looking for means to do just that. Article 50 has not been triggered, the referendum has no legally binding effect, and there is widespread support for the EU in parliament. People will be looking at ways to avoid the exit, without bringing down the democratic structures of the UK and it's possible they may find one.
Personally, I think anything short of a full exit from the EU - at least in the short term - would be a big mistake for the country. Yes, it will do huge damage to our economy, our standing in the world, and our political influence for all the reasons I've spent months arguing but ignoring the result of the referendum would also do huge damage to the politics of the UK and may even have more damaging impacts in the longer term. The EU is important to our nation; democracy is more important.