Is your manager always like this, or has it just been lately? I once worked with a manager who was like this, and it makes me wonder whether yours is getting a ton of pressure from his higher ups. Even if he is, that's no way to motivate his team.

For me, when there was too much to do and not enough time, I've had 1:1s with my old manager and talked about the priorities. For his personality, it helped him to see a list of all the things that I was working on and my expected time frames to be able to complete each item thoroughly and accurately. If your team is feeling rushed, pressured and overwhelmed, then there is a good chance something won't be completed properly and then it needs to be redone and therefore wastes even more time and resources.

So...hopefully your manager can be reasonable (although it doesn't sound like he is). List out priorities and your expectations on how long it will take to get that task done correctly the first time. If he can respect his team's abilities, he should be able to help manage the priorities. If he isn't willing to step back and listen to reason, then as others have said, it may be time to look elsewhere or grit your teeth and do the best you can. Best of luck!