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In Texas, GOP strategist Corbin Casteel said he saw a number of state House races in which candidates spent money late and did well with Election Day voters, but were dragged down by the early-vote results.

“If they had a stronger get-out-the-vote effort during early vote, they could have won,” Mr. Casteel said. “It’s extraordinarily important.”

In Tennessee, state Senate Speaker Ron Ramsey, who came in third in a spirited primary for the Republican gubernatorial nomination, lamented that he didn’t have enough money to get his message out at the kickoff of early voting because he had to make his cash last.

“I would have loved to have an extra $1 million in the bank, and peaked a week before that,” he said.

Early-vote strategies vary wildly.

In Colorado, where early voters were instrumental in Democratic Sen. Michael Bennet’s winning campaign against a strong primary challenger, Mr. Bennet worked hard to bank the early ballots of unlikely voters - those who had never voted in a primary or had done so just once. Sixty-six percent of his early ballots came from this group, according to the campaign.

In Ohio, Republican strategist Mark Weaver said early voting means campaigns have to reach out to voters much sooner, and that means candidates must either “raise more money or spread the peanut butter on the bread a little further.”