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Clinton and Obama have mobilized different parts of their party. She appeals to the blue-collar voters, and Obama has been more successful with affluent, well-educated Democrats

1. What does it mean 'to mobilize different parts of their party"?

2. Can 'the' be removed?

Thanks in advance!
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1. They have inspired them to be active in the political process.

2. Yes. It was used to emphasize the blue-collar workers in the Democratic party; the Republicans have blue-collar workers too. Note that in the Obama portion of the sentence, it specifies Democrats.
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Thanks, GG!