How to make a concise dissertation defence in Math department
I don't think there is a meaningful answer to this question that is helpful across all US math departments and advisors.  There is too much variation in what is expected.  You need to find out what your committee expects.

That said, if I had to answer without knowing your department or committee, I would recommend trying to focus on the big picture but making sure that you spend most of your time explaining your contribution to that big picture.  That's certainly what you'll want to do for job talks, which you're presumably also giving around now.

If the committee is concerned about your understanding of the technical parts of the proofs, they can ask you in the closed exam following the public talk.