Update: As of July 8, 2014, DisplayPort MST support does not exist in any Linux kernel. David Airlie at Red Hat is working on it, and his work is being merged in Linux kernel 3.17. The upcoming Ubuntu 14.10 "Utopic Unicorn" will use 3.16, so DisplayPort MST support "out-of-the-box" is not expected on Ubuntu until 15.04 (yes, nearly a year from now). I will update this answer with instructions on installing the patch set yourself when I figure out how do it and I will have the hardware supporting MST. I have postponed my purchase of Surface Pro 2 due to personal circumstances, so anyone who has MST hardware and Surface Pro 2 is very welcome to go ahead and install a patch set and try it out and/or help Michael debug it, to assure that when the patch does arrive, it will work well on SP2, as right now MST support seems to be tested on Thinkpad T440s and 4K monitors.
You should be able to use two monitors, one way or the other, unless Microsoft relies on some secret sauce (software, firmware or hardware) that won't work with Ubuntu.
Surface Pro 2 ships with either i5-4200U or i5-4300U CPU, both Haswell chips with HD Graphics 4400 GPU. According to Intel, these chips have 4th generation graphics (HD Graphics 4200 and up is 4th, 4000 and 2500 is 3rd) and thus support DisplayPort 1.2.
Apart from graphics adapter support, you will need compatible monitors. These monitors should be DisplayPort 1.2 compatible and feature two DisplayPorts (for input and output). According to this page from DisplayPort.org (click 'DP Displays Multi-Stream' then 'Search') there are currently seven such models:
Or, you could use DisplayPort 1.2 MST hub like this one: not quite daisy-chain, but a solution to connect up to 3 DisplayPort monitors to a single DP 1.2 MST output. The monitors can be regular old-school DP 1.0, according to this answer.