There's some debate over whether this phrase should be tinker's dam - a small dam to hold solder, made by tinkers when mending pans, or tinker's damn - a tinker's curse, considered of little significance because tinkers were reputed to swear habitually.
If we go back to 1877, in the Practical Dictionary of Mechanics, Edward Knight puts forward this definition:
"Tinker's-dam - a wall of dough raised around a place which a plumber desires to flood with a coat of solder. The material can be but once used; being consequently thrown away as worthless."
That version of events has gone into popular folklore and many people believe it. After all, any definition written as early has 1877 has to be true doesn't it?
Knight may well have been a fine mechanic but there has to be some doubt about his standing as an etymologist. There is no corroborative evidence for his speculation and he seems to have fallen foul of the curse of folk etymologists - plausibility. If an ingenious story seems to neatly fit the bill then it must be true. Well, in this case, it isn't. The Victorian preference of 'dam' over 'damn' may also owe something to coyness over the use of a profanity in polite conversation.
That interpretation of the phrase was well enough accepted in Nevada in 1884 for the Reno Gazette to report its use in the defence of a Methodist preacher who was accused of the profanity of using the term 'tinker's dam':
"It isn't profane any more to say tinker's dam. The minister stated that a tinker's dam was a dam made by itinerant menders of tinware on a pewter plate to contain the solder".
The same view was expressed in the Fitchburg Sentinel newspaper in 1874.
The problem with that interpretation is that all those accounts ignore an earlier phrase - 'a tinker's curse' (or cuss), which exemplified the reputation tinkers had for habitual use of profanity. This example from John Mactaggart's The Scottish Gallovidian Encyclopedia, 1824, predates Knight's version in the popular language:
"A tinkler's curse she did na care what she did think or say."
In the Grant County Herald, Wisconsin, 1854, we have:
"There never was a book gotten up by authority and State pay, that was worth a tinker's cuss".
So, we can forget about plumbing. The earlier phrase simply migrated the short distance from curse to damn to give us the proper spelling of the phrase - tinker's damn.