Let me preface with this: I am not a physicist, only an interested party who has thought about the same phenomenon.
I'd like to start by saying that it is possible. Now the two above, longer replies I have read, and, to myself, understand. The reason being begins with suppsoing that the two proposed observers could be left totally independent (say we were using machines of incredible accuracy that could not communicate and thus become the same observer). Now, as above, set one machine to measure position and the other to measure momentum. As mentioned above, the uncertainty principle dictates that the more accurately one measurement is made, the accuracy of the other beings to decrease (uncertainty increases).
Given that each machine is only logging one measurement to the greatest possible accuracy it could achieve, and both do not intend to measure the other property (the machine measuring momentum doesn't measure position and the machine measuring position doesn't measure momentum), then, after they are done taking measurements, you put their logs side by side (assuming that these machines were recording their respective information in sync) you have both the momentum and position of that particular particle over a set amount of time.
I know that the above can be debated with the above statement that the uncertainty principle is not based on the number of observers but the nature of what is being measured. But that is also exactly why it should work. Each observer sees, essentially a different particle, one sees a particle with no momentum and the other sees a particle with no position (only said for the sake of simplicity, believing the accuracy of the measurement to be absolute and thus the uncertainty of the complimentary measure to be absolute), despite, to a third party, to be observing the same particle. Now here's another counter argument: These observers are observing different particles and thus the measurements cannot be compared and treated as if they came from the same particle. However, I would like to mention that it is not these parties (the two observers), who are responsible for taking the measurements, who are comparing the data sets, but a third party who was observing the observers observe the particle, and understands that whatever data comes from those observers is in fact data related to and only to that particle.
This is the part where I pick apart why I said it was 'possible'. And it is for the following reasons:
1) There must be only one possible, observable particle for both observers to measure.
2) You must be able to observe and measure the particle without disturbing the particle's motion.
3) The observers must begin making their measurements at the same time, at the same rate and with the same accuracy.
And because these criteria are hard to meet, particularly number three, it is merely 'possible' (in a theoretical sense) but not practical.
If none of that made sense, please point out any errors or flaws. If your just confused, then ask for clarification.