Couple or more thoughts for you ..The brain gives up long before the body needs too, don't think about the miles before you, but about the miles you have completed, the quickest way to the finish line is to run..
And be in the moment, concentrate on what you are doing, don't worry about what is ahead ...'are you going to need to walk' doesn't matter until you 'need' to walk so don't think about it, if you do need to focus on something start imagining the finish line or that nice long soak in the bath afterwards...distance running is all in the mind
I have the Liverpool Half Marathon on Sunday, only got up to 10 miles in training before I got injured, so I will be just hobbling around but I know I can finish, and so will you. Good luck
When you say you could only 'hack' three minutes, why, was it the weather or road conditions ?
I am guessing that you may have started too fast, so first you need to find a pace you are happy with (you should be able to run and hold a conversation), maybe do a walk / run e.g walk to one lampost then run to another and small increases after that ..two lamposts running one walking etc...ensure you warm up before your run and warm down afterwards hopefully to fend off injuries
8 weeks is doable as you don't have to get to 6.2 miles in training (that's just for the race) aim for 5 miles, with the knowledge on the day/ race conditions will get you to the finish line
Good luck and just take it easy if this is your first race, just enjoy the atmosphere any time you complete is a PB, start towards the back as you don't want to get in the way of the faster runners (besides you will be surprised how many people you overtake)