2006 mustang gt starting problems?

My 2006 GT wont stay started. I can hear the fuel pump turn on and the engine will start but sputter. Which leads me to believe the fuel filter is bad. However I don't understand since it was working fine then after work it just wouldn't stay started as soon as I hit the gas the engine turns off. It seems like its just not getting any fuel but I'm not sure is this a problem with this model? Please help!