Of course you do not resign. If you get layed off, you'll have a package (usually several month's pay). If you resign you get nothing.
Do not worry what other people thinks. I know a lot of people get layed off. Nobody remembers that in 1month.
You hu*****and should encourage you, not blame you. However, on your part, spend more time with family. I do not think you can change your boss' view no matter what you do.