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“We have for a long time considered this to be a competitive race. We’re fully prepared for that,” Ms. Gilbride said. “But it’s a race we expect Senator Smith to win.”

Mr. Smith holds a sizable fundraising advantage, as he raised $9.7 million by the end of the second quarter and had nearly $4.5 million in the bank as of June 30.

Mr. Smith also enjoys considerable personal wealth, which would allow him to tap his bank account to help finance his race if the national and state Democratic parties continue to pump money into Mr. Merkley’s war chest.

Mr. Merkley raised more than $1.42 million for the three-month period ending June 30 - three times what he raised during the first three months of the year. He also had spent $2.2 million by the end of June and finished the quarter with $564,435 cash on hand.