The first rendering is an example of elliptical phrasing. Because the same phrase is repeated in the second line, it's omitted from the first, lest there's the lengthy "And if you want me to [spend my life with you] / I'll spend my life with you."
The second rendering indicates a reciprocity with the "too." The "if you want me too" implies that the singer/speaker also wants the girl he's addressing.
Because the chorus is repeated (the first chorus has some different lyrics, but the iteration with these "And if you want me to(o) / I'll spend my life with you" lines is sung twice), both renderings could be understood in turn.