Meanings
The phrase appears, with no clear meaning, in a 1755 Samuel Foote nonsense prose poem, "The Grand Panjandrum". In the U.S., soap took on the meaning of money (see OED), and so no soap was a denial of money, say in response to a request for some.
It is (or was) a failure.
Example Sentences
1
I hoped to convince my parents to let me go to the party, but it was no soap.
2
I tried to fix my computer, but no matter what I did, it was still no soap.
3
I attempted to repair my car engine, but it turned out to be no soap.
4
I thought I could convince my teacher to extend the deadline, but it was no soap.
5
I tried to persuade my siblings to let me play with them, but it was no soap.
