There is a question dealing specifically with entry to the United States for foreign citizens on the CBP site.
For Mexican citizens:
A visa and passport are not required of a Mexican national who is in possession of a Form DSP-150, B-1/B-2 Visa and Border Crossing Card*, containing a machine-readable biometric identifier, issued by the Department of State and is applying for admission as a temporary visitor for business or pleasure from contiguous territory by land or sea. Mexican citizens using the Border Crossing Card may travel 55 miles into the U.S. - except in the Nogales/Tucson area, where travel to Tucson is authorized.
The Border Crossing Card (BCC) is acceptable as a stand-alone document (by itself) only for travel from Mexico by land, or by pleasure vessel or ferry. Together with a valid passport, though, it meets the documentary requirements for entry at all land, air, and sea ports of entry (to include travel from Canada). Note: You must be a Mexican citizen and a resident of Mexico to have a BCC.
Given that you're traveling more then 55 miles into the country you will need a passport and if your passport is machine readable you shouldn't have to worry about the Border Crossing office reading it. The machine readable format is universal. Plus Mexico is exempt by the US from 6 months past leave date validity requirement.
So if the date says 3/6/2015 and it actually means June 3rd, 2015 then you should be fine but I would renew it anyway.