Whether it will negatively impact your application depends on the schools you applied to. Some will not review your application until it is "complete," meaning secondary submitted, fee paid, and LORs in. Others only require a certain number of LORs to be in before they review it. Likely, this will further delay your application being reviewed, which is far from ideal.
See if there's anyway to get the letters uploaded electronically, as that is much faster and doesn't depend on the USPS.