Albert Barnes Commentary Psalms 78:37

"For their heart was not right with him, Neither were they faithful in his covenant." — Psalms 78:37 (ASV)

For their heart was not right with him - Luther renders this, “Not fast with him.” The Hebrew word means “to fit, to prepare;” and the idea is that the heart was not “adjusted” to such a profession, or did not “accord” with such a promise or pledge. It was a mere profession made by the lips, while the heart remained unaffected. See the notes at Psalms 78:8.

Neither were they stedfast in his covenant - In maintaining his covenant, or in adhering to it. Compare Psalms 25:14; Psalms 44:17. See also Psalms 78:8.