driving uln2803 with 3.3v
Sadly no.
The current for all the outputs has to pass through the VCC pin when driving high or through the GND pin if sinking current when low. As pointed out earlier, the bottleneck in the system is the wire-bond between the physical pin on the package and the actual silicon inside. The connection is through a very fine wire, welded at each end and it will either burn out or overheat the silicon to the point of destruction.
You are also looking at "Absolute Maximum" figures for the chip which are the ones the manufacturer specifies as the "point of no return" in terms of chip reliability. In other words, if you exceed them you almost certainly cause permanent damage. You will note they are generally higher ratings than the normal operating ones.
Try a 2803A, it might just work, if not, you will have to look at power drivers of some sort.
Brian.