Senate Minority Leader Charles E. Schumer is on the hot seat as Republicans try to portray him as the face of the government shutdown and congressional Democrats expect him to deliver something that can be sold as a victory. The New York Democrat has broad support from his caucus and House Democrats for his moves thus far, but he is under pressure not to let the shutdown end without a significant win for his side. Mr. Schumer’s standing in the party took a hit after he declined to use a government funding deadline in March to oppose the Trump administration’s...