You can show your support for him without agreeing that he quit his job.
Go through your finances together - how much do you have in savings, what's your likely income / expenditure while he's job hunting, is there anywhere you can trim short term (e.g. going to interest only mortgage or taking a 6 month mortgage holiday).
Look at what is causing stress with his current job and see if you can work out a way of minimising it or managing it. Is there an option to reduce his hours and reduce his stress levels that way without quitting completely?Could he work from home one day a week to lose the hassle of a commute?
Definitely be proactive with his job hunting to try and get something lined up so he knows he has something to leave to - often just knowing that it's not going to last forever and there is an exit plan in place can relieve some of the stress.
Can you set a time limit on it? Say 6 months, where you will save every penny you can and if he hasn't found a new job to go to, have a savings level that will allow him to quit anyway?
Finally - while you say you've been a SAHM too long and there are few jobs in your field... is there an option for you to return to work even part time? That might allow him to reduce his hours or look for a lower paid but less stress job.
In the main I agree that you shouldn't leave one job without having another one to go to but I know the soul destroying despair of working in a place you hate, knowing you have no choice because 2 small children and your husband depend on you staying there for a roof over everyone's heads and food on the table. In my case, knowing my dh appreciated how much I hated working there and him making my home life as easy and stress free as possible went a long way towards saving my sanity.