The defect of a degraded birth is the result of prarabdha-karma, previous activities that have begun to bear fruit in this life, and this prarabdha-karma can be destroyed by uttering the name of Bhagavan.  The proof of this is stated in Srimad- Bhagavatam (6.16.44): 

 “Even a lowborn dog-eater can be delivered from material existence simply by hearing Your holy name once.” 

It is also stated in Srimad-Bhagavatam (6.2.46):  

“Those who desire liberation from the bondage of material existence have no means of rooting out sin except by the chanting of the holy names of Bhagavan, who sanctifies even the holy places by the mere touch of His lotus feet.  The reason is that when one performs nama-sankirtana (congregational chanting of the Holy Names of Krishna), the mind does not become attached to karma again, whereas when one practices any other means of atonement, the mind is again contaminated by the qualities of passion and ignorance, since the tendencies to commit sin have not been destroyed at the root.” 

Again, in Srimad-Bhagavatam (3.33.7) it is stated:  

“Oh!  What more can be said about the greatness of a person who chants the holy name of Sri Hari?  A person whose tongue utters Your holy names is superior to all, even if he has taken birth in a family of dog-eaters.  His brahminical status has already been established in his previous birth.  Those fortunate jivas who chant sri-hari-nama have already undergone austerities, performed fire sacrifices, bathed at the holy places, followed the rules of proper conduct, and thoroughly studied the Vedas.”