I have always thought that Willie must have been influenced early in his career by Dinah Washington. The phrasing is more jazz influenced than country.
Willie's always been too "wide-band" for country traditionalists. Many of his early songs - Crazy, Funny How Time Slips Away, The Nightlife - are as much jazz standards as country. Luckily, the country music audience is much more willing to accept music from other sources. People may have an image of "narrow-minded rednecks" as the core country audience, but I have found that the opposite is true. If they like you, personally, you can do almost anything.