You can head straight to the immigration office and ask them to extend your visa.
It's not a "visa." But, yes, had the OP taken the matter seriously and visited an office of the INM before the FMM - tourist permission card - expired ... it might have been extended ... if the entry hadn't been flagged for other concerns by Mexico.
You just have to carry your passport, visitor card. You need to prove that you are financially capable of extending your visit. for that you'll need your debit, credit card, or your bank statement.
Sometimes, the INM agents will ask for proof of onward travel ... and a valid credit card or exhibit of cash ... sufficient for the number of days being asked for in an extension request. There's little consistency across-the--board amongst the INM offices/officers, though. Lots of discretion afforded the agents. I've never heard of someone being asked for a bank statement ... except when one of the expat aliens living in Mexico once again lied on their FMM cards (or were suspected of doing so).
Let's not feed the trolls interrupting this discussion. ;-)
LW