The current flowing through each motor winding also must flow through the corresponding output transistor. There is no "chip" output current supply that is separate from the motor winding current.
The ULN2003 datasheet at http://www.datasheetcatalog.org/data.../489337_DS.pdf does allude to the possibility of paralleling two (or more) of the transistors in the package to handle a higher output current. You do have to observe the maximum device dissipation rating, though. There are three unused transistors in the package, but that is not quite enough to double-up on each output.
Alternatively, you could drive some higher-current output transistors from the ULN2003 outputs, but if you're going to go to the trouble of adding supplemental output transistors, then you might as well not even use the ULN2003 to begin with, and simply use discrete darlington transistors that are rated to handle a higher current to drive the motor windings (don't forget the diodes to handle the back emf).