lick and a promise, a - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
A superficial effort made without care or enthusiasm. For example, I haven't time to do a good job of vacuuming, just enough for a lick and a promise. This expression is believed to allude to the quick lick a cat or other animal might give itself and a promise to do more or better at some future time. [Mid-1800s]