It's frustrating- are the kids who have issues with being late or absent still fulfilling the state or provincial learning objectives? The fundamental problem is, of course, that carrots and sticks are terrible motivators for changing people's long-term behavior. The issues that things like detentions and push-ups cause seems to me much greater than the seeming short-term benefits they derive. I'm wondering, if you were constantly late to work and your principal made you do pushups during lunch in the staff room, called your wife or kept you in on weekends it wouldn't increase your intrinsic motivation to be a good professional. If anything, it would create either hostile feelings, cause you to consider that staying late at school is a punishment (when in reality putting the idea of 'being in school = bad' or that exercise = punishment).
I feel you on the motivation factor. I guess its different for every student/class/school.
The problem is that the principal feels these lates/absences will eventually pull down their grades and we can all see the correlation there!
When I have kids who are habitually late I try to understand why it is they're late. There are hundreds of reasons that we could discuss here, but at the end of the day it doesn't really matter. Do the kids consider your class important? Interesting? Crucial? Are the kids having issues at home? Are they 'fashionably late' for a reaction out of you (which leads to a worse problem- the dreaded you vs. them). Fuck, are they late because mom or dad are shitty at getting them to school on time?
Often, I just let it roll off my shoulders. As long as they arent disruptive and settle quickly. The VP on the other hand wants all staff to handle it in house. Hence, you can administer "pushups" if you think it will help.
Talk to the other teachers about the specific kids who are constantly late. Are they late to everyone's class? Only mornings? After lunch?
Problem seems to be school wide, every morning and immediately after lunch classes.