Can you put an operating system on a two gig jump drive"?

Question

Also, how would you go about doing it?

Answer 1

This:
http://en.wikibooks.org/wiki/Knowing_Knoppix/Using_an_external_USB_drive

or this:
http://rz-obrian.rz.uni-karlsruhe.de/knoppix-usb/

Should answer your question.
Since you are using a two gig drive, you can put KNOPPIX on it, which is a very good bootable distro.

Answer 2

Yes, you just need to have it plugged in when you start the install then pick that drive as the install drive. Then, to boot from it you need to set up the BIOS to boot from a USB drive.