Upvote:2
Technically, US citizen must be allowed to enter, even without the passport.
However, the onus is on you to prove that you are a US citizen, and that is difficult without a passport and any other papers. You might be able to enter, but chances are that they don't believe you, especially at the mexican border.
It is clearly the better approach to get the passport sent by Fed-Ex or similar. It will save you spending a lot of time at the border, potentially being detained, or turned back.