“Stop calling when desired result is reached.”
That’s not how it works. Prior to the fielding of a poll, the number of completed surveys is established. Within that are Quota Cells designed to match the geographic area that is being polled.
The poll is not completed until the goals are met.
“Call a known list of liberals until the desired result is reached.”
Most pollsters design a sample frame and purchase the sample from SSI or generate RDD sample in-house. No listed sample is used.
You are assuming an honest poll/polling company. That is a big assumption.
If, OTOH, you understand that many polling companies are not honest, that they will poll for anyone that pays them...and work to satisfy their customers, THEN you will see that you are looking at the distant past where honesty (of a sort) reigned.
Some were caught using established lists in years past. Legislation was passed to make polls more transparent but there is no policing that can keep them honest. Follow the money: “Who is paying for the poll?” We can safely bet that pollsters who work the numbers receive nice gifts months later quid pro quo.