“He can gaze to Washington — as long as he’s focused here,” said Scott M. Stringer, the city comptroller who also stood for re-election on Tuesday.
Michael Morey, another Democratic strategist in New York, added: “The second term, without the necessity of worrying about re-election as New York City mayor, is going to free him to try to do what he tried to do in the first term, which was become a national progressive voice. He will be much more unencumbered.”
Not that Mr. de Blasio has been particularly encumbered of late. The city has pitched Amazon to locate its second headquarters here, but on the day of the submission, Mr. de Blasio blamed the online giant for hurting local retailers. In Manhattan on Monday, he was asked “what exactly” the city would do to lure Amazon, for other cities had offered tax breaks and incentives.
“We offer Amazon the greatest city in the world,” he said.
Likewise, on Tuesday, Mr. de Blasio remained unaffected by would-be critics. Protesters who want to close the jails on Rikers Island far sooner than the mayor’s timeline surrounded Mr. de Blasio’s polling site in Park Slope, Brooklyn, but the mayor arrived through the back door.
Later, after voting, the mayor and his wife, Chirlane McCray, decamped to their favorite neighborhood patisserie. For a half-hour, they enjoyed espresso and pastries at their corner table, interrupted intermittently by selfies.
“Did you vote yet?” the mayor would ask patrons. “We need your vote today.”
On his way out, the mayor said not to expect him to break from routines in a second term, even those for which he has sustained some criticism.
“No changing who we are,” he beamed widely.
With that, he headed down the block, grabbed his gym bag and slipped into the Prospect Park Y.M.C.A.