Dusting off my BS in mathematics to answer this question.
Margin of Error is a very misunderstood term. It does NOT represent the total amount a poll may be off. It ONLY represents how far it is likely to be off based on the size of the sample. It does not take into account the kind of people making up the sample.
For example if your sample is 1000 Democrats, the Margin of Error would be the same as if it were 1000 voters of a more realistic distribution. But obviously the poll would be way off at predicting the outcome, far beyond the Margin of Error.
Specifically a "Margin of Error" is a calculation that assumes a perfectly representative sample (right number of each demographic etc). This is never a safe assumption. But given this assumption the MoE will be the possible range that a "perfect" sample of that size would fall in a certain percentage of the time. I think it usually is calculated as 95% of the time.
In this year's elections, nobody has a good idea how to get a good sampling...and indeed some pollsters seem to be intentionally getting some that are over optimistic for the Democrats.
So "margins of error" were proven to be nothing but figments of the pollsters imaginations in 1996. And so the polls that showed Dole would lose to Clinton by 20% or 18% had so much egg on their faces when he lost by around 8%. A British journalist observing all this wrote that if the polls and media had not been so skewed and slanted against him, Dole/Kemp might have had a chance.