A strike would just hasten GM and Ford's bankruptcy. The management of both companies seems intent on trying to sell vehicles for less than Hyundai and only a little more than Kia. At current prices, I've read that they're currently taking a loss of $200-400 on most of their "Employee Discount" vehicles. Obviously that's a losing strategy unless GM and Ford can reduce their cost structure to the point where it's on the level of the Korean automakers. To do that, they need to completely reorganize, close factories, eliminate all their retired employee pensions, slash jobs, etc., and the only way they're going to do that is through bankruptcy reorganization. I suspect management is deliberately gunning for bankruptcy, and a strike would just play into their hands.
Personally, I think GM and Ford management is utterly incompetent for trying to compete on price rather than value, technology, fuel efficiency, or quality, but management is not going to change their ways barring some kind of miracle.