But if Iowa gives Republicans their biggest reason for hope, Colorado and North Carolina offer reasons for caution, even though Republicans won Senate seats in both. In those two states, the Republican victories appeared to rely on low turnout, and Democrats fared very well among college-educated white voters. In Colorado, Senator Mark Udall, a Democrat, lost by two points in a state that Mr. Obama won by five points. But Mr. Udall ran what was widely considered to be a mediocre campaign, focused relentlessly on Mr. Gardner’s past support for a “personhood” amendment that would confer constitutional rights at conception.

Had young voters and registered Democrats turned out at the rates they did in 2012, Mr. Udall would likely be looking forward to another term, according to an Upshot analysis of voter file data from the Colorado secretary of state.

Mr. Udall maintained nearly all of Mr. Obama’s support among college-educated white voters. He even outperformed Mr. Obama among college-educated white voters, according to exit polls. Jefferson County, a suburban county consisting mainly of well-educated white voters west of Denver, and a bellwether in statewide elections, went to Mr. Udall, narrowly.