No. To say that the Bible says this shows a lack of understanding about the relationship between the old and new covenants

The New Covenant is the “Old Covenant” completed and fulfilled by Christ. Both are one and the same, except one is unfulfilled and the other fulfilled. God’s purpose did not change. Therefore the New Covenant had the same sanction as the first.

Similarly the first covenant purposed to make us in the Image of God as we were originally intended, just as the New Covenant does. Sanctification is recognized as the method by which God makes us like Christ. This is us being remade in the image of God (since Christ is God).

The Abrahamic covenant was also designed to make us in the image of God though a living obedient faith in the perfect and atoning sacrifice (just as James says Faith without works is dead 2:17). We were not able to fulfill the covenant because we lacked faith in the complete and atoning sacrifice that the Abrahamic covenant and the Mosaic covenant pointed to in Jesus as Christ. Thereforth our faith was dead and our works non-existent.

Nonetheless, it is an error to assume that somehow the ‘new Covenant’ is different than the Abrahamic covenant or the Mosaic covenant (which is in Harmony with the Abrahamic covenant) other than to recognized it is the Abrahamic covenant fulfilled (by Jesus) who was gloriously promised in the Mosaic covenant.

Compare [Hebrews 8:8-12] with [Jeremiah 31:31-34].

“Note then the kindness and the severity of God: severity toward those who have fallen, but God’s kindness to you, provided you continue in his kindness. Otherwise you too will be cut off.”