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Opposition political parties in Korea are complaining that the revised agreement gives preferential treatment to U.S. auto manufacturers. But Mr. Lee, who won ratification, said the accord will create “jobs for our workers, expand trade and investments, and overall improve the lives of our peoples.”

Another looming result of the trade agreement that neither nation’s president is mentioning is that the U.S. will export more lawyers to Korea.

The agreement allows U.S. law firms to open up shop in Korea, and several top-100 firms are rushing to tap the market. Covington & Burling LLP, Washington’s largest law firm, is among them.

“That’s exactly because of the [free-trade agreement],” Mr. Cha said. “They could not open before the FTA. It’s going to take a few years for them to get up and running, but it’s certainly a big deal for them. It’s a new market. There’s a lot of business in South Korea.”

As much as Mr. Obama is talking up the agreement with autoworkers, trial lawyers are part of his political base, too.

U.S. food exports also are expected to rise as a result of the accord.

In a poll of 250 wholesalers and retailers released by the Korea Chamber of Commerce last month, 29.1 percent of respondents said they will increase imports of processed foods from the U.S. About 28 percent said they will import more fresh food.