Sending transcripts after deadline?

Hello, I recently applied to Harvard and Cornell using Commonapp. I was not able to send them a lot earlier due to having to wait for a letter of recommendation. I also found out today that the counselors at my school do not send the official transcripts along with the school report, and my school is on break right now so I am unable to contact my school’s records office in any way. If I send my transcripts immediately when I get back will that be fine, or are my applications completely jeopardized at this point?

No, youre fine. In fact, I’m surprised you didn’t submit earlier w/o your letters of recommendation. You don’t need to have that with your app when you submit, after all.
For most of the schools that I have seen, and as I was told by someone who works with Private Liberal Art Schools, all the stuff that is mainly outside of your control (school report, letters of rec, transcript, etc.) are not held to the same deadline as the deadline for the applicant. Why would a college deny a possibly amazing applicant when it was the teachers/counselor’s fault for not submitting on time? They’ll give them a few days extension. However, that does not mean that they should submit a week later. On the contrary, a few days is the rule of thumb.
I have not read anywhere of how much is “a few days”. But I would definitely have your counselor send the transcript as soon as you get to school.
On a personal note, I do hate these January 1st deadlines. Students are notorious for procrastinating, even the amazing ones. I would definitely prefer if these deadlines were held back to before break or after break. After all, some of these schools are closed during break. I don’t see why they would make the deadline when they’re on break if a student has a question concerning the application. Several colleges such Dartmouth and UChicago (I believe) have noticed this and emailed students that they can submit such forms (transcript, letters of rec, etc.) by January 5th, the day that most students will get back to break. More schools should follow this policy, in my opinion.