"You don't inspire these people to go out of their way for you, and you've got everyone wound so tight that there's no joy in anything."
What I would have said is something more like this: "Sir, I fully appreciate the urgency of the situation at hand and that there's no time to build a relationship with the crew right now, but you'll get a lot more out of them if they feel like you care. Drive them hard, but also give them some breathing room in return."
Jellico was pushing hard relentlessly. He had to wait for Deanna to let him know how the crew feels. And rather than collaborating with Deanna on what to do about it, he just shoves the whole "morale boost" project onto her shoulders. "Get it done."
There is a difference between being firm and being callous. I just finished watching this episode again and there's a nuance to Jellico's personality. He doesn't make much effort at all to smooth things out. He's firm, coarse, and unforgiving. No, he doesn't need to mimic Picard to get the crew to work for him. But all he needed to do was just be a little less abrasive. That's what I see.