Underpayment of Extension?

Related to another question of mine, I can't do an OIC or Installments because I'm paying off a bankruptcy, yet I owe taxes which I can't afford to pay. One suggestion was to file an extension and try to come up with the full amount by October, initially paying what I can April 15th. But does anyone know what happens in October when I file and it shows that I underpaid in April? Trying to figure out if I'm penalized worse or less for filing the extension.