Some Democratic and Republican senators are newly optimistic that the government shutdown, which has dragged on for more than a month, might soon come to an end.

They believe Tuesday’s elections, among other factors, will encourage senators in both parties to find a way to reopen the government.

“The election’s kind of the first report card on Trump,” Sen. Mark R. Warner (D-Virginia) said. “I hope it will frankly empower some of my Republican friends to move from talking about things to actually finding their way to get to some compromise.”

Democratic victories in the New Jersey and Virginia governor’s races could make Republicans question their shutdown strategy, putting fresh pressure on GOP lawmakers to negotiate an end to the shutdown, Warner said. Republicans, meanwhile, argue that

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