If you search internet for AVR309 or USBTiny you can already find drivers to interface ATtiny2313 running software USB implementation. Thay all are based on Igor Cesko IgorPlug documented in AVR309. (for example AVR ISP programmer at USBtiny-based AVR Programmer)
In the same AVR309 app note there is source code for roomier ATMega8 chip as the 2k flash on 2313 is too tiny to implement standard USB HID Communication Device Class for virtual COM port that would not require additional drivers.
Absolutely the closest implementation to what you are looking for is AVR-CDC for ATTiny45 and could be found here: AVR-CDC but 2313 version implements only limited subset of serial interface functions.
Vikas, I agree with you that it would be very tempting to get it working as USB-RS232C solution as ATTiny2313 is the cheapest AVR chip that has full-duplex UART (unlike half duplex USI implementation found in other ATTiny's) but it is, probably, technically next to impossible.
Did you consider other chips and / or modular design? If you are billed per PCB area significantly then you could actually save costs by breaking out any SMD parts onto a smaller boards and connecting them to a larger single layer base board.
I have bought FTDI breakout board from SparkFun and could use it with either Arduino Pro Mini or breadboarded ATMega 168 chip that I have.