Why does it take so much fuel to start a jet engine?
The first figure, 1 litre per mile, is very wrong. The second, 39 to start, is most probably the fuel required for a warm up from a cold start. The Abrams tank weighs 62 tonnes, so you won't get 1 mile on a litre. Its fuel consumption is quoted as 0.6 mpg, or 1.66 gallons per mile, which is 6.3 litres per mile. Quite a difference. 

The engine is the Honeywell (previously Lycoming) AGT 1500. It has a two spool gas generator, with a two stage power turbine. It features a heat exchanger through which the HPC exit air flows, to preheat it from the exhaust gas, prior to combustion, to improve engine efficiency.

The engine has a tactical idle that keeps it running at 1500 rpm instead of 950 so that it can rapidly accelerate from a stationary position if needed to avoid or engage a hostile force. In tactical idle it consumes 30+ gallons per hour, instead of 10 at the non tactical idle setting.

It's stated that "in 1990, Project on Government Oversight in a report criticized the M1's high costs and low fuel efficiency in comparison with other tanks of similar power and effectiveness such as the Leopard 2. The report was based on data from U.S. Army sources and the Congressional record."

Some critics say the tank fuel consumption is so poor, that in combat, it has to often wait for the fuel supply logistics to catch up. Other reports deny this. (See paragraph at the very top of the page).

The M1 Abrams was chosen after a competition in June 1973, between the Chrysler Corporation and the Detroit Diesel Allison Division of the General Motors Corporation to build prototypes of a new tank designated M1, and later named the Abrams tank. In November 1976, it was announced Chrysler won the competition.


  The M1 was faster and more maneuverable than its predecessors in the M60 series, while offering a lower, smaller silhouette. Besides the substantial gains in performance, the Textron Lycoming AGT-1500 turbine engine was far more reliable than the diesel tank engines then in use with the Army. There was still another benefit. The engine change, despite a penalty in fuel consumption, also resulted in much quieter operation, so much so that soldiers encountering the tank in early maneuvers started calling it "Whispering Death".


The Abrams wikipedia page also states a figure of 6.3 liters per mile, and also states the value of 38 liters to start. As suggested by user3528438 (thank you), the 39 litres (10 US gallons) is quite probably the fuel required to complete a warm up from a cold start. At the tactical idle setting, this would be the fuel consumed in about 15 to 20 minutes.