Regarding the Islamic ruling of performing Umrah while in debt, we would like to quote Dr. Monzer Kahf, a prominent economist and counselor, who said the following:

If the loan you have taken is interest-based and can be settled by the amount you will spend on `Umrah, the priority should be to settle this loan because ridding oneself from haram always has priority over doing further acts of worship. This is especially so since `Umrah is not an immediate obligation according to the Hanbali school and it is not an obligation at all (just desired) according to the other three major schools of Islamic thought.

If the debt is to an Islamic bank and you have other resources to pay it on time, there is no need to pay it instead of  performing `Umrah.