If the data really comes in continuosly, at full speed with no breaks, then you are in real trouble, since eventually you will overflow any size buffer you put in your PIC (which is limited by RAM size).

Is there some way you could send at a baud rate higher (like 2X) than you are receiving? They you would have a chance.

It would help a bit if you would run a faster oscillator as well (20MHz). And *WHY* are you not using an 18F series part?