I’ve found a couple of explanations for this one, none of them burdened with much by way of evidence.

I’m thinking of the meaning of “The operation was a success, but it’s still touch and go”.
Etymonline gives us a tag like game, which is not the same sense. There is also the aircraft landing technique, when the pilot will intentionally abort a landing as part of training, called a touch and go.

I’ve seen a definition that will keep the CANOEists happy http://www.defence.pk/forums/members-club/79527-etymology-common-expressions.html
(this site is a ripper for the canoeists). I’ve also seen sites that refer to horsedrawn carriages touching wheels, but not tangling, enabling them to ‘touch and go’.

It’s an old phrase. Any suggestions on its beginnings? What/who was touched?

Here’s a thread from the old board. No definitive answers as to whys and wherefores but some interesting hydraulics.  Edit: Let me revise that in light of oeco’s post below (I’d missed OED’s explanation of ‘touch’ in Dr T’s cite).

Dr. T noted this sense in that old thread but I thought I’d give the full citation:

3. A risky, precarious, delicate, or ticklish case or state of things (such that a mere touch may cause disaster); a narrow escape, ‘close shave’.

1815 R. Wardlaw Let. in Alexander Life vi. (1856) 166 ‘Twas touch and go—but I got my seat.