Hayworth has expressed interest in running against McCain, but he has not announced that he will do so. The former Congressman got 43 percent support in the survey of likely Republican primary voters, while McCain got 45 percent. Four percent went to former Minutemen leader Chris Simcox.
McCain leads among the state's Republican women, while Hayworth leads among men.
Rasmussen points out that a September poll found that while 75 percent of Republican primary voters expect McCain to win the nomination, 61 percent feel he has lost touch with the members of his party.
Nearly three in four Republicans nationwide say elected Republicans in Congress have lost touch with party members.
As for McCain's running mate, Sarah Palin, Rasmussen has found that 59 percent of Republican voters say she shares the values of Republicans across the country.