If we're making a legitimate push to meet a commitment, I'm not going to sit behind a laptop checking boxes while the field carries all of it.
If I can bring them lunch, have it delivered. Take them out to dinner one night. Tell the foreman or superintendent, “Take the guys out. Put it on the company card.”
Better yet, get out there.
Roll your sleeves up. Spend some time with them. See what they're dealing with. Help where you can. Let the crew see that meeting this commitment is important enough that leadership is willing to be present for it too.
Those things don't erase the workload. They don't make fatigue disappear. But they tell the people doing the work something important:
We see what you're doing.
When people are being pushed day after day and all they hear from management is more, faster, when will you be done?, eventually that pressure starts working against you. Morale drops. Frustration builds. Small mistakes start showing up. Keep applying pressure without giving anything back and eventually you've created another problem.
That's why I don't think the only choices are “push them harder” or “miss the date.”
Leadership has a role in getting that crew across the finish line.
Recognize the effort. Remove whatever obstacles you can. Give them something back. Get in the field. Make sure they understand why the deadline matters and that the people asking for the extra effort aren't disconnected from the people actually providing it.