I know, I know, the solution to burnout is to slow down and take some time off.
What do you do when you're exhausted, your brain is fuzzy, and you just plain have to meet a hard deadline in a few days? You have obligations to your team and your company and yourself that just can't put off.
It's all well and good to say you'll take a week off once the deadline is met, but how do you keep your brain operative and your mind focused enough to read and write code for those intervening 3 days when you can barely read a sentence of plain English text without having to go back over it 3 times to extract any meaning?
For working weekends, I've adopted a policy of roughly one weekend a year. That's how often I believe true emergencies happen (at least for most situations; Google SRE need not apply).
Look, if it's an isolated incident, take some breaks, find something to distract and relax you, get sleep. If it's a second or third attempt to get the team to crunch hard, quit.