Is it possible for a Mexican Citizen to get a Mexican Passport in one day?

Yes, if you are in Mexico and you have all your documents needed, you get your passport the same day that you apply.
First of all, you have to go to www.sre.gob.mx , which is the page for Secretar铆a de Relaciones Exteriores and look for all the documents that are required, you also need to bring pictures, photocopies of your previous (expired) passport, if you had one, and also from that web page you have to print a form that you take to any bank to make your payment, before you show up at any delegation of SRE.
If you have already made your payment and have your documents and pictures ready, you should go to SRE early (they open at 8), and you can pick up your passport early in the afternoon.

no.

Maty is completely right, she already gave you all the information you needed to know...... you CAN get a passport the same day you apply for it if you're a mexican citizen.

Yes you can my friend!

it really does depend on the state. i know for a fact that aguascalientes has an extremely quick turn around, and if they aren't out of the documents, they can get it to you while you wait. but...i don't know if every state can be this fast, i have heard that aguas has exceptional speed

no you need to go fill in some papers and your passport will be given to you in a day or 2. its about $200 pesos for the whole thing

EDIT- never mind, matt is right. but it depends where you go to get iy. once i went to a little town outside queretaro and it took me about 2 day to get it but if you go to another place you can get it the same day. my bad :)

Yes is possible, but it may change from state to state. In my case I had to make a line of more than 80 people who were there from 4:00 AM on a saturday. They only give like 100 tickets and anyone who doesn't get a ticket cannot get the passport that day. see www.sre.gob.mx