Backing

When fishing for Steelhead I have had several instances where the fish made a run and I had 90 ft of fly line off the reel.  I was getting down to the backing and was afraid to allow anymore line to go off.  So I stopped the fish and in doing so my tippet broke.  This occurred during high water conditions when I was wading and I couldn't move up or down the creek. 
 
Could I have let the fish take off some of the backing and bought some more time to land the fish?
 
Thanks
 

 As long as your knot to fly line to backing is good i would've let em run.  I keep atleast a 100 yards on most of my fly gear.  The only exceptions are my 3 wt which only has 50 yards of 20lb and my 10 weight which has 200 yards of 30lb.  Let em run but if you can its best to try and catch up with the fish because the weight of your fly line in the current will put more stress on your tippet and can cause it to break or a fish to pull the hook...

Yes, you can use the backing to play a steelhead.  In fact, with the normal size 14-16 hooks and 3X-4X tippet that we use, you should count on it.  Modern large arbor reels hold the same amount of fly line as conventional reels, but the extra capacity is there for - backing.  I use two colors of backing on my steelhead rods.  The 100 yards of outer backing connected to the fly line is chartreuse (fly line is ivory).  The backing tied between the spool arbor and the outer backing (maybe 30 yards or so) is fluor red .  If I am playing a fish in the chartreuse backing, it's OK.  But if the fish gets me into the red backing, it is time to break him off, chase him, or just pull hard and hope.  Note that good arbor and Albright knots are essential.  They should be retied every season and checked every few trips. 

Put your rod tip down in the water and to the downstream side. Put very little pressure and start reeling slowly to gain line and speed up reeling as needed. This gives pressure on the fish from the downstream side do to the surface current pulling your line. They will swim away from the pressure, back upstream towards you. Once he is back to a comfortable spot countinue fighting the fish like you normally would. Remember to use different angles to maintain max pressure on a fish. I see to many people with their rod straight up in the air with a big bend in it struggling as the fish just sits in the current. You think you are doing something correct but you're not. When the fish is just sitting still he is resting.