Yes, it is possible to replace the threshold and the sill. Door sills and thresholds are sold at the big box stores and can be installed in 1 hour to half a day. Make sure the new sill is fully supported with shims and such to get the maximum benefit.
I think you are talking about the sill needing to be replaced. That is the piece that is attached to the bottom of the frame that bears your weight. Not to be condescending or persnickity, the threshold is the added piece under the door to make the weather seal and the transition from the sill to the floor inside.
My sincere apology if I have read it wrong.