He described the song as "a hard one for me to even get through without breaking down the first time" because of how personally he felt that it expressed his love for Shires.
The Bluegrass Situation describes the song as " Solemn, stripped-down, and slow, it floors listeners with its stark vulnerability and the strength of its romance as Isbell unfolds his love for Amanda Shires".
[3] Steve Leggett, in his review of the album for AllMusic, called "Cover Me Up" a "beautiful opening love song".
It sets the tone for the remainder of the album, which is given equally to the promise of romance and the ever-looming possibility of suffering, both self-induced and arbitrary.
[13] After a controversy surrounding a video of Wallen shouting a racial slur in February 2021, Isbell announced that he would donate his songwriting royalties to the Nashville chapter of the NAACP.