Devils are faced with extinction due to factors like roadkill, and Devil Facial Tumor Disease, a fast spreading cancer that forms tumors, preventing consumption of food. ​​​​​​​

“A disfiguring and deadly facial cancer has slashed Tasmanian devil numbers by up to one-half in the past decade. ‘It's an aggressive cancer that is spreading rapidly and killing animals within 6 months,’ says Menna Jones, a zoologist at the University of Tasmania in Hobart” (Bostanci)
This quote illustrates the crisis nicely, describing just how quickly the devil population has come perilously close to extinction.

“Since the project started we have received reports of over 7,000 road-killed devils (between 350 and 450 each year)” (Save)
This provides more insight into why the devil faces extinction, describing how roadkill has affected the population. 
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Save the Tasmanian Devil Program, A road-killed Tasmanian devil 

“Field research indicates that between one-half and one-third of the 150,000 devils that lived in Tasmania 10 years ago have been lost. According to a report released in January, the disease is now present across at least 65% of the island” (Bostanci)
Tasmania is researching how the spread has affected the population of devils. This is relevant because it shows drastic change in level of concern for the fauna of the island.

“Populations in which DFTD has been observed for several years have declined by up to 80% (approximate, due to low sample size in recent years). There is no evidence to date of the decline in devils stopping or the prevalence of the disease decreasing.” (Save)
Due to the previously discussed factors, Tasmanian devils are in deep trouble.
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What is being done about the situation?