i've noticed this recently on my 2006 mustang GT automatic with ~54k miles

when im just cruising at like 40mph, the car starts jerking back and forth....thinking its transmission problem, but the tachometer isn't moving, its keeping cosntant idle ~2k rpm....so not sure, but i'm gonna get the tranny fluid changed just to be on the safe side. any other ideas? what do you guys think is going on? I know my tires are really bad and need to be replaced, but i dont have the money right now can tires cause this problem? I do oil change every 3k miles and use chevron with techron. also i last changed the fuel filter at 30k miles.