A failing fuel pump can cause low fuel pressure in the fuel lines which means your engine will get less fuel than it requires to start or run properly.
A failing fuel pump can cause hard starting, rough idling, engine sputtering, loss of engine power, engine surging and a decrease in Gas Mileage.
A bad fuel pump can also cause your cars engine to not start at all especially if the fuel pump is not working at all.
A good auto shop should be able to check the fuel pressure coming from your fuel pump and determine whether it's completely bad or is failing.