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After oil company Chevron gave $2.5 million to a House Republican super PAC this month, the Democratic Congressional Campaign Committee asked online donors to counterbalance the corporate money and raised $10 million in five days, with a goal of making House Speaker John A. Boehner “shed a tear.”

That’s given Democrats in tight districts a huge boost, with the committee spending 15 times the amount its Republican counterpart doled out this week.