On a Wing and a Prayer

This phrase originated with the WWII patriotic song Coming in on a Wing and a Prayer, 1943, by Harold Adamson and Jimmie McHugh, which tells of a damaged warplane, barely able to limp back to base:

One of our planes was missing
Two hours overdue
One of our planes was missing
With all its gallant crew
The radio sets were humming
We waited for a word
Then a noise broke
Through the humming and this is what we heard

Comin' in on a wing and a prayer
Comin' in on a wing and a prayer
Though there's one motor gone
We can still carry on
Comin' in on a wing and a prayer

What a show, what a fight, boys
We really hit our target for tonight
How we sing as we limp through the air
Look below, there's our field over there
With just one motor gone
We can still carry on
Comin' in on a wing and a prayer

Adamson and McHugh wrote several patriotic songs in World War II and were awarded the Presidential Certificate of Merit by President Harry Truman.

The phrase hit a chord with the public and there are many references to it in US newspapers from 1943 onwards. It was taken up by Hollywood and a film - Wing and a Prayer - was released in 1944.

The allusion to a strcken aircraft limping home was probably influenced by the earlier term 'winging it', which refers to actors struggling through parts that they have recently learned in the wings of a theatre.

The phrase is sometimes given mistakenly as "on a whim and a prayer", or "on a wink and a prayer".

http://www.phrases.org.uk/meanings/on-a-wing-and-a-prayer.html