How large a factor was the economy failing and Rome facing bankruptcy to their downfall when you compare it to the likes of political corruption and the rise of Christianity?
Economy of the period is analysed in the book by Bryan Ward-Perkins, Fall of Rome and the end of civilization (Oxford UP, 2006).The author gives abundant evidence that the fall of the empire was accompanied by a collapse of economy, material production and infrastructure in general. The evidence is based on contemporary accounts and archeological data.
However it is not completely clear whether the collapse of the economy was the reason or a consequence of the fall of the empire. My impression from the evidence presented in this book is that it was rather a consequence. The reason for destruction of economy was apparently collapse of administration, as a result of civil wars and invasions.
EDIT. Another recent book on the subject, Adrian Goldsworthy, The fall of the West. The death of the Roman superpower, (US title: How the Rome Fell), 2009 attibutes the fall of the empire to the constant internal struggle for power. It was so intense that the emperors cared more about their own survival than for the survival of the empire. The result was invasion of the tribes, which in turn led to the collapse of the central government and of the economy.
There is no consensus among historians as to what exact reasons lead to the downfall of the Roman Empire. There are varying different theories on this matter, but at least Edward Gibbon in his 1776 book The Decline and Fall of the Roman Empire, gives a well-researched and more importantly, well-referenced account. According to him, barbarians from the outside were majorly responsible for the fall of the Roman Empire:
Significant events include the Battle of Adrianople in 378, the death of Theodosius I in 395 (the last time the Roman Empire was politically unified), the crossing of the Rhine in 406 by Germanic tribes, the execution of Stilicho in 408, the sack of Rome in 410, the death of Constantius III in 421, the death of Aetius in 454, and the second sack of Rome in 455, with the death of Majorian in 461 marking the end of the last opportunity for recovery.
Economics were better than ever. Both the Imperial Romans and their successors, the Byzantines, were very wealthy. Unfortunately for them, it takes more than wealth to keep an empire together.
The thing to remember is that by 450 Rome did not really exist anymore in its original sense. All of the old families were gone or dispersed. There were no Cornelii, no Julii, no Scipii, all the old gens were gone. The city was full of Greeks, Africans, Germans and Judaeans. Nobody was even Latin anymore. The original Latins were a very serious, austere, strict people. The Romans of the 5th century were all on public welfare and wasted their time going to games, theaters and prostitutes. The army was a joke, mostly populated with foreign mercenaries. There were all sorts of wierd religious cults like the cult of Mithras. Economic activity wasn't the problem; the problem was that Rome was not a coherent group of noble people any more.