I am not certain from where this expression comes, but visualize a miner discovering a vein of gold buried in the earth. Think of the miner "tapping into" this vein. Equally fortunate would be the politician who garnered 70 million votes.

"Tap" in this case is similar to a faucet, and "tap into" means to get access to a resource -- such as water, petroleum, natural gas, etc. but can be used more broadly too. Your example sentence sounds a little bit strange, but I think the author means the politician has access to a big supply of "political power."

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