Following Spieth's triumph at Chambers Bay last weekend, McIlroy's lead in the world rankings is down to just 1.72 points.
"Jordan is putting it to Rory and that can only be good for Rory. He has to step up to the plate," McGinley told BBC Sport.
"As well as he played to come fourth in the Masters and ninth at the US Open, he left himself too much to make up."
Spieth also won The Masters in April.