2002 Chevrolet Cavalier Somethings cutting out...

When I accelerate the car seems to be cutting out. I press the gas and the car will do like a sputter like the gas my be cutting in and out.. but if i press the gas really slow it doesn't do it. It normally does it when It's been running for a while...

New TPS, Fuel filter, spark plugs and wire are only 5 months old. (I bought the good wires and plugs)

Also, Since i have bought the car 8 months ago, I've notice that i have kinda a poor idle... its really low idle and sound a little rough. and only once i has died for the low idle....

Thanks,
John