You have to unload the stored momentum from the reaction control wheels or they will saturate when they reach their maximum rotational speed. At that point, they're no longer able to maintain pointing. There are two different techniques used to unload the wheels: firing thrusters or using magnetic torquing. On the DSCS-III satellites I used to control, the onboard controller unloaded the wheels once a day. It would automatically warm up the thrusters and fire the necessary pulses to reduce the wheel speed. Other satellites, especially those flying in low orbit (including the Hubble, which has no propulsion system) use magnetic torquing. Every orbit or so, electromagnetics are activated to interact with the Earth's magnetic field, causing a torque to unload the wheels.

I don't know which technique is used on Cassini. Saturn has a magnetic field, but Cassini is in a high orbit. Off hand, I'd guess they use thrusters for this job. However, the amount of propellant needed to unload the wheels is quite small, so that isn't a likely operational constraint on Cassini. Other factors, such as reaction control wheel failure (a frequent problem on the Hubble and the ISS) are more likely to cause problems. You need at least 3 functioning wheels to completely control attitude. After that, you're back to thrusters to control attitude. SOHO has operated in this mode for some time now, so that isn't necessarily a show stopper.

In the end, other system failures may be more likely to kill the mission in the long term than propellant or even reaction control wheel problems. Cassini is built with a lot of redundancy, but eventually systems will die. If they're critical ones, such as TT&C, well, then it's all over. It also depends on how much propellant is used during routine maneuvering to visit the various moons of Saturn. Finally, there may come the day when the government decides that the amount of new science that can be gathered isn't worth the cost. That might happen if the mission stretches on for many years past the 4 year design point. If memory serves, that happened when the Apollo Lunar Surface experiments were turned off.