According to the liner notes of the Everly Brothers set, "Since You Broke My Heart" was recorded in 1959. This is a few years before "Please Please Me," so the chronology allows for such an influence, and the Beatles' live on the BBC cover of "So How Come (No One Loves Me)" illustrates their familiarity with the Everlys. The liner notes of the Everly Brothers set even mention Paul McCartney specifically: "there was equally no question that the likes of Paul McCartney had been hugely influenced by their Fifties output."
According to Lewisohn's The Complete Beatles Recording Sessions (p. 20), "Please Please Me" was originally a Roy Orbison-type song. Lewisohn quotes George Martin's description of it as "very dreary... very slow [with] bluesy vocals." Martin "told them that the song could be much better if they increased the tempo and worked out some tight harmonies." Apparently, whether consciously or not, the Beatles patterned their harmonies for this particular song on the Everlys' in "Since You Broke My Heart."