I'm Canadian so you can ignore my comment if it doesn't apply. First of all, the regulation is that the US asks for the passport to return to the US, not the other way round. Even if it has not been enforced yet for those of you who have commented, it is something ANY border guard can enforce at any time, on either side of the border. If I were making this trip for surgery, I would not be taking any chances.
Also somebody asked about having different names on different documents. I lived in Mexico for several years and I can assure you that Mexican bureaucracy has a very hard time with names not matching. If you have a birth certificate that is not your current name I would carry the connecting document as well (eg. your marriage certificate).