Yesterday, at the close of the Mass commemorating the 10th anniversary of 9/11, we sang the national hymn, "God of our Fathers." The tune is not bad, except for the trumpet intro which gives it a harsh militaristic overtone.
But, the song is rarely sung and it does not speak to the religious sensibilities that have long characterized the American people. There is a better alternative, one that concluded the ceremony at the Kennedy Center: Amazing Grace. This hymn is the most frequently sung at funerals. This hymn is the most frequently sung at national prayer services. It functions are our national hymn de facto.
The only other competition would be the Battle Hymn of the Republic, but that should be our National Anthem.