As Ned Lamont basks in his Democratic primary victory in Connecticut, another antiwar underdog is trying to assume the same role of political giant-killer in next month’s elections in New York, though against much bigger prey: Hillary Rodham Clinton. But while Mr. Lamont united liberals and used $4 million of his own money to win his primary, Jonathan Tasini is struggling on a shoestring campaign to rise above his 12 percent standing in the polls, even as he hawks a message of left-wing anger over Iraq to an electorate that is more liberal than Connecticut’s. Mr. Tasini has qualified for...