[What you need to know to start the day: Get New York Today in your inbox.]

When Bill de Blasio embarked on his long shot campaign for president, he hoped to convince voters that his record as New York City mayor argued for a chance to prove he could pursue progressive policies from the White House.

Even if he failed, Mr. de Blasio wanted to move the Democratic conversation to the left, focusing on income inequality and issues like early childhood education, where he scored his biggest success as mayor.

Instead, the challenges Mr. de Blasio faces in the largest city in the country are starting to define his presidential bid, and possibly his political future.

With the mayor falling short in fund-raising and in polls, he needed an impressive performance in Detroit on Wednesday, in the second round of Democratic debates. Instead, the debate put his critics on national television.