Now is the time to sell to your manager, so they can sell to their manager, why you and your team are mission critical, and are working to keep the lights on.
The time to sell to your manager was six months ago or earlier.
I recognized that this was going to be happen last year, pulled my manager aside and explained how dire the situation and how we needed more visibility in the company. He thought I was being paranoid, but agreed with the general benefits of improving things. We've made some promising changes, but layoffs haven't happened yet so no idea if it worked.
If layoffs are happening leadership and the board are already drawing up plans for layoffs and nobody is thinking about you they're thinking of an org chart and a list of compensation to figure out what makes the most sense from a big picture perspective. They're thinking of a product road map and who is needed to make their current strategy work. Nothing you can do now will change that.
The time to convince leadership you were mission critical is well before you realize that layoffs are coming.
All that said, layoffs are more arbitrary that most would like to believe. Don't stress yourself out too much thinking about what you can do to safe your self/team. You never had much control over this situation.
As a manager I feel responsible for knowing this at all times. I don't want to be sold to. Just give me consistent work at the expected quality at whatever pace you can sustain.
Perhaps I'm fooling myself, but I think I can definitely tell when people are burning the candle at both ends to compensate for any perceived shortcomings. That doesn't really impress me. In fact, it worries me, as I want consistency and sustainability. Don't burn out or begin making lots of mistakes.
I can't promise this is how all managers think. And there's definitely companies that are perfectly happy for you to work 60 hours when being paid for 40. Either they don't care, or are ignorant of the qualitative cost of that.
I'm very fortunate to work somewhere that gives me a reasonable amount of autonomy for how to ensure my team delivers quality work on-time. One of the main reasons is that the company doesn't MBA us to death by doing things like, "they're on-time! Give them 20% more work next time!"
Not proposing to grovel, but to make sure the value is being conveyed with data to back it up. Hopefully this already being done, and it doesn't hurt to continue doing so.
