This is not, ah, going to be terribly convenient.
Your GSM module will indeed pull bursts of up to 2A. I can't be bothered finding out it's worst case average consumption; if it were to pull a constant 2A, you'd need a 6F (yes, farad) capacitor to hold >=3.4V for 2 seconds, if you started off at 4. But you will also have to contend with the ESR of the capacitor, because the module does not permit the voltage to droop below 3.4V. So if your cap has a 1 ohm ESR - not uncommon for supercaps - you sacrifice a volt right there, and you're dead in the water before you even began.
You may want to describe why you want a two-second backup supply, so people can give you better suggestions than "slap a big honkin' cap on it".