Nonresponse bias
The error that arrives when the people who did not answer differ from the people who did, in a way that matters to your question.
Nonresponse bias occurs when answering is related to what you are measuring. If non-respondents differ in relevant ways, collecting more responses from the same kinds of people may leave the bias unchanged.
People with strong views may be more willing to answer than those with little interest. A margin of error does not account for this kind of bias; it describes sampling uncertainty.
Practical defences are unglamorous: shorten the survey, ask at a moment people are willing, follow up with non-responders rather than collecting more from the same crowd, and compare what you know about responders and non-responders on any field you hold for both.
Where it goes wrong
Treating a large sample as a representative one. Volume from a self-selected pool makes the bias more precise, not smaller.