2001 Chevy Cavalier ABS light is on.

Should not have anything to do with the fuel pump.
However if a speed sensor is at fault it could send messages to the computer that could affect the running of the vehicl such as fuel mixtures and transmission operation. I recommend you check for any codes stored in the computer to determine if it is a speed sensor or the ABS unit itself acting up. You did not supply enough information about what is going on to do much more diagnosis. You may want to reply with mor info about what is happening.