I'm still w*rking, but ran into a similar problem over the summer, when I tried to get prequalified for a mortgage. At the time, I owed about $100K on my current house, and the monthly payment was around $1847. It had been an HELOC that reached the end of its draw period, and converted to a 10-year mortgage, so the monthly payment was comparatively high.
Anyway, ideally I want to be able to buy a new house, without it being dependent on selling the current house. That way I could move at my own pace, and could hold out for a better price on the current house, rather than possibly get talked into a fire-sale price, just to get out of it, for fear of losing out on what might be my dream home.
The mortgage company, however, had an issue with me carrying that current mortgage. Even though I only owed $100K, they were focusing on the monthly payment. I asked them, what if I payed it down? Their response is that would change nothing, because while that would reduce the principal and get it paid off sooner, it wouldn't change the monthly payment.
Nevermind the fact that I had the assets to pay off the mortgage, plus pay cash for just about any house I was in the market for. They didn't care about that, only that monthly payment.
I guess it'll soon be a moot point though, because with the way the market took off, I decided to pay down the mortgage anyway, and should have it wiped out completely within the next two months. Still, it makes me a bit worried about my chances of getting a mortgage once I'm retired. So, my current plan is to hold out and keep the j*b at least until I've landed a new house, with a mortgage.