Every single mention of debt or borrowing in the Bible portrays it as something negative and not to be desired. This is a clear indication the debt should not be the norm for a church (or for an individual Christian).
There are two very big problems in terms of church debt from a Biblical perspective. The first is that debt presumes upon the future. James 4:13-14 says "Come now, you who say, 'Today or tomorrow we will go to such and such a city, spend a year there, buy and sell, and make a profit'; whereas you do not know what will happen tomorrow. For what is your life? It is even a vapor that appears for a little time and then vanishes away." When a church borrows money, they are presuming that they will have the money come in in tithes and offerings so that they can pay that debt back. They do not know what will happen to the economy, and if half of their congregation suddenly becomes unemployed, they will definitely see a drop in tithes and offerings. This could lead to an inability to repay their debt, and the Bible states that “the wicked borrow and do not repay” (Psalm 37:21). Some people say that this is "stepping out in faith", but doing something that God's word directly advises against doing (i.e. going into debt) is not a matter of faith, it is a matter of presumption.
Secondly, Proverbs 22:7 states that "the borrower is servant (or slave) to the lender". When a church goes into debt, they are putting themselves/their congregation in the position of a servant to a secular financial institution. The only master that a church should be serving is God. They certainly should not be serving a bank.
Furthermore, when a church rushes out and uses debt a solution to meeting a "need", they often deny God the opportunity to show Himself mighty in the way that He can provide. The majorly expensive Chrystal Cathedral in California was built without one cent of debt. Churches would often be better off by waiting on the Lord rather than looking at how they can finance an expense. Is God always going to provide? No, but in the cases where He does not provide it may mean that He was not wanting the church to do what they were planning to do in the first place.
I could probably go on and on about this subject, but instead I will close by saying that I do not think it is a good idea for churches to go into debt, and from what I read in His word, God doesn't seem to think so either.