[touch up variant may be influenced by British touch up, ''to grope a woman'']
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with touch go
touch and go
Extremely uncertain or risky, as in It was touch and go after the surgery; we were not sure he'd survive it, or It was touch and go but they finally gave me a seat on the plane. This idiom implies that a mere touch may cause a calamity.
[ Early 1800s