DENVER – They had $10 million in contributions, a barrage of advertising and support from the usually warring factions of the educational establishment. But Democratic leaders in this swing state were dealt a stinging defeat on Tuesday as voters resoundingly rejected an effort to raise taxes by $1 billion a year to pay for a sweeping school overhaul.

The outcome, a warning to Democrats nationally, was a drubbing for teachers unions as well as wealthy philanthropists like Mayor Michael R. Bloomberg of New York and Bill and Melinda Gates, who pumped millions of dollars into the measure, and it offered a sharp rebuke to Gov. John W. Hickenlooper and the Democratically led legislature, who have recently tugged Colorado to the left with laws on gun control and clean energy.

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