Terminating Transmission Lines with a Resistor
2 MHz gives a 500 ns bit period. 1 foot foot of ribbon cable would be about 1.5 ns (or less) propagation delay or 3 ns round trip. 

Adding termination resistors will increase power consumption, and the CMOS-style chip you're using isn't really designed to work with a terminated line. 

A cleaner solution is to slow down your rise and fall times. You could easily transport 2 MHz signals with 50 ns rise and fall times. One way to get slower edge times is to use a different chip than the "ultra-high speed" part you chose. Another would be add a series resistor at the driver outputs. This resistor doesn't have to exactly match the transmission line characteristic impedance, just slow the edges when combined with the line's capacitance. As an added benefit, if someone comes along later and wants to use your circuit with a shorter ribbon cable (and less capacitance), the loss from the series resistor will still help to kill any ringing quickly so its died down by the time (250 ns later) that your receiver samples the signal.