Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If you find yourself unable to perform the sacrifice because of being burdened by debts, you need not worry about it. Allah does not burden any soul with duties that it has no strength to bear.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
The Prophet (peace and blessings be upon him) said, “If the days of Dhul-Hijjah draw near and one of you wishes to offer sacrifice, let him not take anything of his hair or nails before the sacrifice has been done!” (An-Nasa’i)
While scholars and jurists of all persuasions are in agreement that udhiyah on the days of `Eid Al-Adha is a great tradition, the majority of them are of the opinion that it is a highly recommended sunnah and not a mandatory duty of faith.
The purpose of this ritual is two-fold: First, it is a commemoration of Ibrahim’s sacrifice. In other words, by doing so we are challenged to interiorize the spirit of sacrifice demonstrated by the great Prophet Ibrahim (peace and blessings be upon him) in our life.
Second, it accords us an opportunity to feed the poor and the destitute while commemorating the event; Islam insists that in the days of feasting no one should be prevented because of lack of means from participating and partaking the joyful experience of `Eid.
In light of the above, sacrifice is a great sunnah of `Eid Al-Adha It should be done by those who can afford it. The Prophet’s words mentioned above certainly imply, as some scholars have pointed out, that it is not a mandatory duty but a recommended act, for if he had intended to make it a firm order, he would certainly stated the matter more firmly and decisively.
To conclude: If you find yourself unable to perform the sacrifice because of being burdened by debts, you need not worry about it. Allah does not burden anyone with duties that he or she has no strength to bear.
Allah Almighty knows best.
Excerpted, with slight modifications, from: www.islam.ca