The cat will probably survive.
An overdose of antibiotic puts the animal's body under more strain. Remember that the basic principle of an antibiotic is to lightly poison the animal, counting on the fact that the animal survives this poison better than the infection does. The dosage is adjusted to be high enough to kill off the targeted microorganisms while being low enough not to do significant damage to the patient. Increasing the dosage forces the body to work harder to detoxify the chemical; specifically, it is likely to consume more of the liver enzymes which play that role.
But there is usually plenty of safety factor in the standard dosage.
To answer more specifically we would need to know exactly which antibiotic, in which formulation, at which dosage; the size and health of your cat, what illness is being treated, and so on. Your vet has all this information, so you should ask them rather than us. You may also want to ask them whether you should continue the original dosing schedule, switch to the new schedule, or get one more pill so the treatment runs for the recommended number of days.
Summary: don't panic, do ask your vet.