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But Mr. Sessions denied that Friday’s Labor Department report that showed the unemployment rate increased slightly in May added pressure on Congress to quickly pass a long-term transportation bill, saying he will support such a measure “only if it’s a good bill.”

“The job loss is directly related to the president’s polices that he has placed, and continues to place, on businesses … it’s not related to a transportation bill,” he said.

Rep. Patrick J. Tiberi, an Ohio Republican and a transportation bill conference committee member, also bristled at Democratic pressure to accept the Senate bill.

“Should I just give my voting card to [Ohio Sens.] Rob Portman and Sherrod Brown and say … you guys decide?” Mr. Tiberi said. “How are we obstructing if they won’t negotiate with us?”