Aetna Inc. and Humana Inc. face resistance from the Justice Department to their proposed $34 billion merger and an uphill battle persuading antitrust enforcers the deal won’t harm competition, according to people familiar with the matter.The insurers on Friday met with top government officials in a late-in-the-game attempt to make their case that the deal has public benefits and won’t hurt consumers, and that they could address competitive concerns through asset sales, people familiar with the matter said.Aetna and Humana recently floated a package of potential divestitures to possible buyers, and drew bids from major insurers—a point they made in Friday’s meeting, according to a person with knowledge of the matter.

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